I'm having trouble getting started with this proof. Any help is appreciated...

If $\displaystyle f[0,1]\rightarrow \mathbb{R}$ is continuous, then, $\displaystyle \int _{0}^{1}f=lim_{n\rightarrow \infty}\sum_{k=1}^{n}f(\frac{k}{n})(\frac{1}{n})$.

My thinking is that I need to construct step functions for $\displaystyle f$ but I guess I don't know where to go with that.