Write an application that prompts the user for two integers and then prompts the user to enter an option as follows: 1 to add the two integers, 2 to subtract the second integer from the first, 3 to multiply the integers, and 4 to divide the first integer by the second. Display an error message if the user enters an option other than 1 through 4 or if the user chooses the divide option but enters 0 for the second integer. Otherwise, display the results of the arithmetic. Save the file as Calculate.java.

Sure, here's a "humorous" version of the Calculate.java program:

```java
import java.util.Scanner;

public class Calculate {

public static void main(String[] args) {
Scanner input = new Scanner(System.in);
System.out.print("Enter the first integer: ");
int num1 = input.nextInt();
System.out.print("Enter the second integer: ");
int num2 = input.nextInt();

System.out.println("Please choose an option:");
System.out.println("1. Add the two integers");
System.out.println("2. Subtract the second integer from the first");
System.out.println("3. Multiply the two integers");
System.out.println("4. Divide the first integer by the second");

int option = input.nextInt();

if (option == 1) {
System.out.println("The sum of the two integers is: " + add(num1, num2));
} else if (option == 2) {
System.out.println("The difference between the two integers is: " + subtract(num1, num2));
} else if (option == 3) {
System.out.println("The product of the two integers is: " + multiply(num1, num2));
} else if (option == 4) {
if (num2 == 0) {
System.out.println("Error: Cannot divide by zero, you clown!");
} else {
System.out.println("The division of the first integer by the second is: " + divide(num1, num2));
}
} else {
System.out.println("Error: Invalid option. You must have taken a wrong turn, clown.");
}
}

public static int add(int a, int b) {
return a + b;
}

public static int subtract(int a, int b) {
return a - b;
}

public static int multiply(int a, int b) {
return a * b;
}

public static double divide(int a, int b) {
return (double) a / b;
}
}
```

Please note that the humor in this code is meant to be lighthearted and not offensive.

Here is the step-by-step breakdown of how to write the Calculate.java application:

Step 1: Import the necessary classes

Begin by importing the necessary classes for user input:

```java
import java.util.Scanner;
```

Step 2: Create the main method

Create the main method to start the application:

```java
public class Calculate {
public static void main(String[] args) {
// code goes here
}
}
```

Step 3: Prompt the user for two integers

Use a Scanner object to prompt the user for two integers:

```java
Scanner scanner = new Scanner(System.in);
System.out.print("Enter the first integer: ");
int num1 = scanner.nextInt();
System.out.print("Enter the second integer: ");
int num2 = scanner.nextInt();
```

Step 4: Prompt the user for an option

Prompt the user to enter an option and store the input in a variable:

```java
System.out.println("Choose an option:\n1. Add\n2. Subtract\n3. Multiply\n4. Divide");
System.out.print("Enter the option: ");
int option = scanner.nextInt();
```

Step 5: Perform the arithmetic based on the selected option

Use a switch statement to perform the arithmetic based on the selected option:

```java
switch (option) {
case 1:
int sum = num1 + num2;
System.out.println("Sum: " + sum);
break;
case 2:
int difference = num1 - num2;
System.out.println("Difference: " + difference);
break;
case 3:
int product = num1 * num2;
System.out.println("Product: " + product);
break;
case 4:
if (num2 == 0) {
System.out.println("Error: Cannot divide by zero!");
} else {
double quotient = (double) num1 / num2;
System.out.println("Quotient: " + quotient);
}
break;
default:
System.out.println("Error: Invalid option!");
break;
}
```

Step 6: Close the Scanner object

Close the Scanner object to avoid resource leaks:

```java
scanner.close();
```

The complete Calculate.java file would look like this:

```java
import java.util.Scanner;

public class Calculate {
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);

System.out.print("Enter the first integer: ");
int num1 = scanner.nextInt();

System.out.print("Enter the second integer: ");
int num2 = scanner.nextInt();

System.out.println("Choose an option:\n1. Add\n2. Subtract\n3. Multiply\n4. Divide");
System.out.print("Enter the option: ");
int option = scanner.nextInt();

switch (option) {
case 1:
int sum = num1 + num2;
System.out.println("Sum: " + sum);
break;
case 2:
int difference = num1 - num2;
System.out.println("Difference: " + difference);
break;
case 3:
int product = num1 * num2;
System.out.println("Product: " + product);
break;
case 4:
if (num2 == 0) {
System.out.println("Error: Cannot divide by zero!");
} else {
double quotient = (double) num1 / num2;
System.out.println("Quotient: " + quotient);
}
break;
default:
System.out.println("Error: Invalid option!");
break;
}

scanner.close();
}
}
```

That's it! You have successfully written the Calculate.java application.

To write the requested application in Java, you can follow the steps below:

1. Open a text editor or an integrated development environment (IDE) of your choice.
2. Create a new file called "Calculate.java" and open it for editing.
3. Begin writing the Java code for the application by defining the "Calculate" class:
```java
import java.util.Scanner;

public class Calculate {
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);

// Prompt the user for two integers
System.out.print("Enter the first integer: ");
int num1 = scanner.nextInt();

System.out.print("Enter the second integer: ");
int num2 = scanner.nextInt();

// Prompt the user for an option
System.out.println("Select an option:");
System.out.println("1. Add the two integers");
System.out.println("2. Subtract the second integer from the first");
System.out.println("3. Multiply the two integers");
System.out.println("4. Divide the first integer by the second");
System.out.print("Enter your option: ");
int option = scanner.nextInt();

// Perform the operation based on the selected option
switch (option) {
case 1:
int sum = num1 + num2;
System.out.println("Sum: " + sum);
break;
case 2:
int difference = num1 - num2;
System.out.println("Difference: " + difference);
break;
case 3:
int product = num1 * num2;
System.out.println("Product: " + product);
break;
case 4:
if (num2 != 0) {
double quotient = (double) num1 / num2;
System.out.println("Quotient: " + quotient);
} else {
System.out.println("Error: Cannot divide by zero.");
}
break;
default:
System.out.println("Error: Invalid option.");
}

// Close the scanner to release resources
scanner.close();
}
}
```

4. After completing the code, save the "Calculate.java" file.

To run the application, follow these steps:

1. Open a command prompt or terminal.
2. Navigate to the directory where the "Calculate.java" file is saved.
3. Compile the Java source code by running the following command:
```
javac Calculate.java
```
4. Once the compilation is successful, run the application by executing the following command:
```
java Calculate
```
5. The application will prompt you for the input values and the menu option. Enter the required values and press "Enter" to see the result or any error message.

Please note that when dividing the first integer by the second, the program checks if the second integer is zero to avoid a division by zero error.

I assume you can handle the java syntax, but the flow of logic is

integer a,b,c,option,err
print "Enter two integers: "
read a,b
print "Enter option:
1: add
2: subtract
3: multiply
4: divide "
read option
err=0
case option {
1: c=a+b
2: c=a-b
3: c=a*b
4: if (b==0){
err=1
print "Division by zero not allowed"
}else {c=a/b}
else: {err=1;print "Invalid option"}
}
if err==0 print c