I want to find some function $f(y)$ such that $$\int_R[f(y)\ dx + x \cos y \ dy] = 0$$
for all closed contours $R$ in the $(x,y)$ plane.
My thoughts:
I am thinking of an opposite function something like $-\cos y$, such that when integrated by $x$, gives $-x\cos y$ which will obviously give 0. But I feel that the question cannot be this simple, and I've not used any knowledge of scalar/vector fields which I think I'm supposed to.