This is possibly a dumb question (please bear with me): the integration would be taken from a to be, correct? Could you post an example of this equation in use, please?
So the in the equation for the winding number/index of a curve
I(\gamma, z) = \frac{1}{2i\pi} \int\gamma \frac{1}{ζ-z}dζ
where \gamma : [a, b] → ℂ and z is an arbitrary point not on \gamma, what exactly does ζ represent?