Hey people.

Given a continuous function f(x) in the interval [a,b] , I need to prove that

$\displaystyle \lim_{n\to\infty} \frac{b-a}{n}\sum_{k=1}^{n}f(a+\frac{k(b-a)}{n}) = \int_a^b f(x)dx$

I think I should do it somehow through Riemann's Integral defnition and/or use Riemann's sums , but I tried to play with it for a while and I haven't gotten anywhere....

Any ideas how should I start proving this?

Thanks in advance!