It is not always very easy to use the definition of the Reimann sums for the computation of definite integrals. We rather prefer using the anti-derivatives of fucntion for this job, i.e., we try to find a function such that on , and then compute , which gives . The computation of the Reimann sum requires in general a high knowledge of sum-difference equations theory.

For instance, you may take a look in the following post, where I have explained the way for the computation of (for ) by means of the Reimann sum (post by me). You may study the following post, for computing the Reimann sum for (post by Laurent).

It seems hard to do that for when (as in your case).

bkarpuz