Solution
= Solution
Choose $r>0$ so the closed disk centered at $a$ of radius $r$ lies in $U$. The <Cauchy integral formula> gives
$$
f(a)=\frac1{2\pi i}\int_{|z-a|=r}\frac{f(z)}{z-a}dz.
$$
Parametrize $z=a+re^{i\theta}$; then $dz=ire^{i\theta}d\theta$ and the denominator cancels. Thus
$$
\boxed{f(a)=\frac1{2\pi}\int_0^{2\pi}f(a+re^{i\theta})d\theta.}
$$