Great, so far. But now you go off in the wrong direction insofar as you are asked, not to directly evaluate the limit of these Riemann sums as , but just to evaluate the corresponding integral.

The result seems ok (to me, that is). But you have done more work than you were asked to do. In other cases, it may be a terrible amount of work to evaluate the limit of the Riemann sums directly, instead of evaluating the corresponding integral.

Assuming all of that is correct, the lim as n approaches infinity is 1/2. However, I've spent a lot of time looking at this problem and might be completely off track.

Thanks