Suppose $\displaystyle f \in R[0, \pi]$. Prove that the sequence

$\displaystyle a_{n}=\frac{\pi}{n}\sum f(\frac{k\pi}{n})$

converges to $\displaystyle \int f$.

Note that the sum is from k=1 to n, and the integral is from 0 to pi.

Can anyone at LEAST give me a starting point for this? I have no idea where to even begin this...