(a) State and prove Morera's Theorem.

(b) Let $D$ be a domain and for each $n \in \mathbb{N}$ let $f_{n}: D \rightarrow \mathbb{C}$ be an analytic function. Suppose that $f: D \rightarrow \mathbb{C}$ is another function and that $f_{n} \rightarrow f$ uniformly on $D$. Prove that $f$ is analytic.