1. Evaluate the integrals
2. Let be the vertices of a closed quadrilateral such that traverses in counterclockwise direction (abusing notation, we shall write for that curve) show that is 0 for (C-minus Box) and 1 if is an interior point of (Hint: do not attempt to parametrize ..)
here (post #8 with long proof), that if is a tiny circle around still inside then . And so the winding number is .