Riemann sums can be tedious. Lotsa algebra to contend with.

Youa re correct,

Therefore, with the right endpoint method:

So,

Expand this out and get:

Now, remember the sums of the squares and sums of the integers formulas?.

Sub those in and you'll be entirely in terms of n. Then, take your limit and you should get the solution. The same as if you did it the quick integration way.