Let $U \subseteq \mathbb{C}$ be a D5008: Standard open complex set such that

(i) | $f : U \to \mathbb{C}$ is a D5635: Standard-continuous complex function on $U$ |

(ii) | $F : U \to \mathbb{C}$ is a D5005: Complex function primitive for $f$ on $U$ |

(iii) | $\gamma \subseteq U$ is an D5023: Oriented complex curve |

(iv) | $\gamma$ is a D5646: Closed complex curve |

Then
\begin{equation}
\int_{\gamma} f(z) \, d z = 0
\end{equation}