I need to..

Show that a continuous function $f \colon [a,b] \to \mathbb{R}$ with the properties $\forall x \in [a,b] f(x) \ge 0$ and $\int\_a^b f = 0$, must be identically 0.

Now i can see why this is true. Its continuous hence 'smooth' between any two distinct points, meaning the integral would not be equal to 0 unless the function is 0 itself, right? But im not quite sure how to translate this.