Verified answer

4π

C = {(x,y)| x^2 + y^2 = 4}, write I = {(x,y)| x^2 + y^2 <= 4}. According to Green's theorem

∫ [over C] (y-x)dx + (2x-y)dy =

∫ [Over I] {∂(2x-y)/∂x - ∂(y-x)/∂y} dydx =

∫ [Over I] {2 - 1} dydx =

∫ [Over I] 1 dydx =

= 4π