Suppose that $\displaystyle f: [a,b] \rightarrow \mathbb{R}$ is continuous and $\displaystyle f(x) \geq 0 $ for all $\displaystyle x \in [a,b]$. Prove that if $\displaystyle \int^b_a f(x)dx=0$, then $\displaystyle f(x)=0 $ for all $\displaystyle x \in [a,b]$.

Attempt

I had attempted to do this problem by contradiction, except I did not understand how to finish the problem. I would appreciate a few helpful hints on this one.