Both answers are correct.
d/dx[ (x+y)^2/2 ] = d/dx[ x^2/2 + x*y + y^2/2 ] = x + y
d/dx[ x^2/2 + x*y ] = x + y
The ambiguity lies in the constant of integration. In the first case the constant of integration ends up being y^2/2.
If you really want to enforce that the constant of integration is zero then do:
F = int(x+y,x,0,x)
expand(F)
