# Theory of Complex Variable. A Question?

I have read a book about Complex Variable and I arose a doubt: Let $f$ be a continuous function on an open ($\Omega$) of C. Suppose that $f$ verifies the thesis of Cauchy-Goursat theorem for any triangle whose edges are contained in $\Omega$.

Is $f$ holomorphic in $\Omega$? Does primitive $f$?

I don't know if I explain well. Thank you,beforehand.

• actually, they have primitives on simply connected domains. the function 1/z is holomorphic on $\mathbb{C}-\{0\}$ but it has no primitive on $\mathbb{C}-\{0\}$ – Glougloubarbaki Feb 3 '13 at 15:24