Cauchy's integral formula

Statement

Let $U \subseteq \mathbb{C}$ be an open set and let $f : U \to \mathbb{C}$ be holomorphic on $U$. Let $c \in \mathbb{C}$ and $r > 0$ be such that the closed disc $\{z : |z - c| \le r\}$ is contained in $U$. Then for each $a \in \mathbb{C}$ with $|a - c| < r$, $$f(a) = \frac{1}{2 \pi i} \oint_{|z - c| = r} \frac{f(z)}{z - a} \, dz,$$ where the integral is the circle integral over the circle $|z - c| = r$.