Question

I got two ways for answering Integral sin(x)cos(x)

The answers were 1/2sin^2(x) + c and -1/2cos^2(x)

Is it possible to solve the integral by using the method sin(2x)=2sin(x)cos(x)
Sin(x)cos (x) = 1/2sin(2x)

Integral sin(x)cos(x) dx
= integral 1/2sin(2x) dx
=1/2 integral sin(2x) dx
=1/2*1/2(-cos(2x)) + c
= -1/4cos(2x)+c

Please correct me if I'm wrong