- Results returned by int do not include integration constants.
If you need a constant of integration, then add one yourself.
"why does the indefinite integral shows incorrect result??"
What leads you to say that the results are wrong?
6*cos(t/2)*sin(t/2) - 4*cos(t/2)^2
3*cos(t/2)^2 - 3*sin(t/2)^2 + 4*cos(t/2)*sin(t/2)
3*cos(t) + 2*sin(t)
Looks consistent to me.