Let $f:[-1,1] \rightarrow \mathbb{R}$ be a continuous function. If $\int_{-1}^{1} x^{2n}f(x) dx = 0$, what can you say about f?

Question

Let $f:[-1,1] \rightarrow \mathbb{R}$ be a continuous function. If $\int_{-1}^{1} x^{2n}f(x) dx = 0$, for all $n = 0,1,2,..$ what can you say about f?

I have seen a similar proof for $\int_{0}^{1} x^{n}f(x) dx = 0$ where f =0, but I am lost for this one. In a similar proof, they used the Weierstrass approximation theorem.