For each of the following, evaluate C . a) C is the topological boundary of the rectangle

For each of the following, evaluate ∫C ω.
a) C is the topological boundary of the rectangle [a. b] × [c, d], oriented in the counterclockwise direction, and ω = (f(x) + y) dx + xy dy, where f: [0, 1] → R is any continuous function.
b) C is the topological boundary of the two-dimensional region bounded by y = x2 and y = x, oriented in the clockwise direction, and ω = yf(x) dx + (x2 + y2) dy, where f: [0, 1] → R is C1 and satisfies ∫10 xf(x) dx = ∫10 x2f(x) dx.
c) C is the topological boundary of a two-dimensional region E which satisfies the hypotheses of Green's Theorem, oriented positively, and ω = ex sin y d y - ex cos y dx.