Let f be holomorphic in D and let $\gamma$: $I$ $\rightarrow$ $D$ be a continuous path. Then anti-derivative of $f$ along $\gamma$ exists and is defined up to a constant.
The assumption here is to use the fact that a locally constant function defined on a connected set is constant on the whole set. And then use that to prove the above. But I do not know where to continue from there. Can someone offer some assistance?