Integrate a symbolic piecewise function

I would like to integrate an expression that includes a piecewise function. The expression is as below in code MuPAD code I attempted which does not give an answer:

assume(a0,R_):
assume(a1,R_):
assume(a2,R_):
assume(a3,R_):
assume(b1,R_):
assume(b2,R_):
assume(b3,R_):
assume(b1 > -0.25):
assume(b2 > -0.25):
assume(b3 > -0.25):
PWise := piecewise([y >= 0.5, (y-0.5)^b2], [Otherwise, -(abs(y-0.5))^b2])
simplify((int)(expand((a0 + a1*(y^b1) + a2*PWise - a3*((1 - y)^b3))^2),y=0..1))

Could someone help please? Thanks