Contour Integrals and Path Independence

Let γ be a curve in ℂ. Suppose that it is parametrized by a continuous complex-valued function z = z(t) for all t in [a, b] such that

(1) z(t) has a continuous derivative on [a, b],

(2) z′(t) ≠ 0 for all t in [a, b],

(3) z(t) is one-to-one on [a, b].

Then we call γ a smooth arc…