lim n-infinity (1/n)(sin pi/n +sin 2pi/n + sin 3pi/n +...+sin npi/n) ?
Recall:
$\displaystyle \int_a^b f(x)\,dx=\lim_{n\to\infty}\left[\frac{b-a}{n}\sum_{k=1}^nf\left(a+k\frac{b-a}{n} \right) \right]$
We are asked to evaluate:
$\displaystyle \lim_{n\to\infty}\left[\frac{1}{n}\sum_{k=1}^n\sin\left(\frac{k\pi}{n} \right) \right]$
So, let:
$\displaystyle a=0,b=1,f(x)=\sin(\pi x)$
Can you finish?