Prove that the following sequence converges, and find its limit.

$\displaystyle a_n=\frac{1}{n^3}\sum_{k=1}^nk^2cos(\frac{k\pi}{n} )$

I'm stuck on just determining what function this is...

I know $\displaystyle b-a=1$ and (I think) $\displaystyle a=0$ so the integral is from 0 to 1. Any other help on this?