1. How does it possible for ∫sin(x)cos(x) dx to have two different solutions, namely (1/2)*(sin2x)+c and -(1/2)*(cos2x)+c, so that would bring to (rediculous) conclusion that sin2x+cos2x=0?
2. Integration by substitution makes use of differentials (not simply derivatives), thus is it purely anti-derivative?
Thank you in advance