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**Dinkydoe** The Cauchy Integral formula states the following:

Suppose $\displaystyle U\in \mathbb{C}$ is an open set and $\displaystyle f$ is holomorphic on $\displaystyle U$. Let $\displaystyle z_0 \in U$ and $\displaystyle r>0$ such that $\displaystyle \overline{D}(z_0,r)\subset U$. Let $\displaystyle \gamma:[0,1]\to U$ be the $\displaystyle C^1$ curve $\displaystyle \gamma(t)=z_0+r\cos(2\pi t)+ir\sin(2\pi t)$. Then $\displaystyle f(z)=\int_\gamma \frac{f(\zeta)}{\zeta-z}d\zeta$ for $\displaystyle z\in D(z_0,r)$

Now I have to show the Cauchy-integral formula is valid if we only assume that $\displaystyle F\in C^0(\overline{D})$, with $\displaystyle D$ some disc, and $\displaystyle F$ is holomorphic on $\displaystyle D$

I'm not sure if I understand what must be shown here exactly. Can someone clarify this a little?