ThmDex – An index of mathematical definitions, results, and conjectures.
Proof P3178 on R1564: Oriented complex curve integral of continuous function with a primitive on open set
P3178
Applying R1558: Second fundamental theorem of complex integral calculus yields immediately \begin{equation} \int_{\gamma} f(z) \, d z = F(z_0) - F(z_0) = 0 \end{equation} $\square$