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.