Given $f(x,y) = sin(y-2x+1)$ on the rectangular domain $R = [0, 1] \times [-1, 1]$, how is symmetry used to explain why the double integral of $f(x,y)$ over this domain is $0$?
Past attempts I used were "freezing" $x$ or $y$, but I do not understand where to go from there. We are specifically asked to justify why this double integral evaluates to $0$ using symmetry instead of integrating by brute force.