Suppose $\mu$ and $\nu$ are positive measures on the Borel $\sigma$-algebra on $[0, 1]$ such that 

$\int fd\mu=\int fd\nu$

whenever $f$ is real-valued and continuous on $[0, 1]$. Prove that $\mu=\nu$.

I have no idea how to deal with this question. How should I do?