Can anybody give me some link which proves that winding number is an integer in complex analysis. In most of the links I found they approached in assuming that $$s \mapsto \int_{0}^{s} \frac {\gamma'(t)} {\gamma (t)-a}\ dt$$ is continuous on $[0,1]$ and differentiable on $[0,1]$ except possibly at junction points where $\gamma$ is closed contour with parametric interval $[0,1]$ and $a \notin \{\gamma \}$. I don't understand this thing clearly. So I want a proof which has some clear discussion. Please help me by giving it if there is any.
Thank you in advance.