You are being asked to perform a numerical integration. Add up the values of f(x) at x= 1,2,3,4,5 and 6 . Multiply the sum by the interval, 1.
Then do it again at x= 1/2, 1, 3/2, 2,. ...6, and multiply the sum by the interval, 0.5.
If you use the average of left and right endpoints, you will be using the trapezoidal rule. It should be more accurate approximation to the integreal