probability theory - Expectation of Random Variable and Indicator Function

I have to do the following problem:

Let $X$ be a random variable in $\mathcal{L}^{1}(\Omega,A,\mathbb P)$. Let $(A_n)_{n\geq 0}$ be a sequence of events in $A$ such that $\mathbb P(A_{N})\xrightarrow[n\rightarrow\infty]{}0$. Prove that $\mathbb E(X\mathbb{1}_{A_n})\xrightarrow[n\rightarrow\infty]{}0$.

I'd appreciate any help.