$D\subset\mathbb{R}^{2}$ is an arbitrary bounded open set with $C^{1}$ boundary whose perimer P is finite. Let $f\,:\,\mathbb{R}^{2}\longrightarrow\mathbb{R}$ be a given $C^{1}$ function satisfying $|f(x,y)\leq1$ for all (x,y) in D. Trying to show $|\int\int_{D}\frac{\partial f}{\partial y}(x,y)dxdy\,|\leq P$
So this is of the exact form for green's theorem where f is really our P for Pi + Qj. the other term is 0 so $\frac{\partial Q}{\partial x}$ is 0 but does not imply Q = 0, so we still have a $\int Q\, dy$ term how do I find that?