Maximizing the difference between two definite integrals

I have a multivariable piecewise function:

z(x,y) = y(50 - y -|10-x|) where y(50 - y -|10-x|) > 0

0 elsewhere



I want to maximize (with respect to y) the integral WRT p of z(10,y) - integral WRT p of z(15,15)