I am still working on this problem. So the problem seems to be the interpretation of the integral

Now evaluating this integral is messing me up. I definitely see that if and . So the part that is still not clear to me is how to get the interval and then the . This problem is making me feel quite dumb.

EDIT: One issue I am seeing is that when I can't see which part of the piecewise function I am suppose to be using. Which of course corresponds to the interval .