In Stein's Text, he provided the following proof to show the existence of a primitive on an open disc domain,
I am confused, why can we not take the straight line $\gamma'_z$ path connecting $0$ and $z$ and define, $$ F(z) = \int_{\gamma'_z} f(w) \, dw $$
The argument then proceeds similarly by applying Goursat's Theorem and continuity. Is there anything wrong with this method?