Can someone tell me if the following proposition is true ?
Theorem If $u=g + i h$ is a holomorphic function in $\Omega\subseteq \mathbb{C}$ and $\Omega$ is simply connected, then $v(z)=u(w)+ \int_\gamma \,g_x(z)-ih_y (z) \,dz$ is a primitive function of $u$ (where $w\in \Omega$ is fixed and $\gamma$ is some path from $w$ to $z$).
(I have come across (the implicit use of) this proposition by reading about something not really related to complex analysis and since I know very little about it, if wondered if it actually would be true taken out of context like this. I also wouldn't mind a proof, if it is true and someone would have the time.)