probability - Show $mathbb{E}(X) = int_0^{infty} (1-F_X(x)) , dx$ for a continuous random variable $X geq 0$

If $X$ is a continuous random variable with density $f_X$ and taking non-negative values only, how do I show that $$\mathbb{E}(X)=\int_0^{\infty}[1-F_X(x)]dx$$ whenever this integral exists?