If you expand (x^2-2)^2/4 you get x^4/4 - x^2 + 1
Although this looks different from x^4/4 - x^2 you have to remember that indefinite integrals are only defined to within a constant, so really, doing the integration your way you should have had x^2/4 - x^2 + k1 and the calculator should have had (x^2 - 2)^2/4 + k2 where k1 and k2 are (different) constants, related by k1 = k2+1.