Integration function generates different result by a same expression

A same expression in two style will be integrated in two different results, why ? and which result is correct ?

    syms a b c x

    y1=a*x+1+a*(b-c);
    y2=1+a*(x+b-c);

    >> int(y1)
    ans =
      (a*x^2)/2 + (a*(b - c) + 1)*x

    >> int(y2)
    ans =
      x + (a*(b - c + x)^2)/2

and obviously they are not equal.

    >> expand(int(y1))-expand(int(y2))
    ans =
      a*b*c - (a*c^2)/2 - (a*b^2)/2

Answer 1

[Mischa Kim]

Tiger, this is because these are indefinite integrals. Solutions to indefinite integrals can differ by a constant. If you make them definite integrals by specifying integration limits, you will get the same answer. Something you can check with isequal, which will return 1 , for true. Or simply compute the difference.

int1 = int(y1,x,0,1);
int2 = int(y2,x,0,1);
isequal(int1,int2)