almost sure convergence of positive random variables with bounded expectation implies uniform integrability?

Question

Let $X_n$ be a sequence of positive random variables that converge almost surely to a constant $a$, and have bounded expected value $\mathbb{E}X_n=\mathbb{E}|X_n|<C$ for some constant $C$ and all $n$. Does this imply that $\mathbb{E}X_n\rightarrow a$?