Let $a \neq b\in \mathbb{C} $ and $U := \mathbb{C} -[a,b] $
Let $\Gamma$ be a cycle in $U$. The following equality is true?
$$\int_{\Gamma} \frac{1}{(z-a)(z-b)}dz=0$$
I saw it some notes of a friend. I know it's true for every cycle $\Gamma$ that is homologous to zero in $U$. But what about the others cycles?