I have the following integral to maximize but I don't know what to do with this $f(b,y)$ in the first integrand:
$$ F=\intop_{a}^{b}[f(b,y)+\intop_{a}^{b}f(x,y)dx]dy $$ a and b are constants. Do I treat $f(b,y)$ as a separate function? Thanks!
UPD A more useful expression of the same problem would be the following: $$ F=\intop_{a}^{b}\intop_{a}^{b}[G(f(x,y),y)+H(f(b,y),y)]dxdy $$