ABSTRACT
In order to prove Cauchy’s integral theorem we will need several technical results. In the first of these we establish that for any function f : D → C that is differentiable on the open set D, and any parametrized contour C ⊂ D, the integral of f along C is equal to the integral of f along a rectangular parametrized contour P ⊂ D consisting of only vertical and horizontal segments.
