Theorem: Let f be a holomorphic function on a disc U, then there exist a function g such that g is the primitive of f and for every closed path gamma.

Proof.

Define

Then define the path from to by t and from z to by , so that t and k forms a circle.

Then the integral over t and k are equal and the integration is independent of path.

Now, I don't really understand why they have to be equal, and what does "independent of path" means, would someone please explain?

Thank you!