I was considering periodic functions that were Differentiable at every point in$\mathbb{R}$, but I realize that a function only has to be
Differentiable at all points in its domain to be considered Differentiable.
One important consequence of the theorem is that path integrals of holomorphic functions on simply connected domains can be computed in a manner familiar from the fundamental theorem of real calculus: let U be a simply connected open subset of C, let f: U → C be a holomorphic function,
and let γ be a piecewise continuously Differentiable path in U with start point a and end point b.