What is the integral of the function f(x) = sin 2x?

The given function is
[tex]f(x)=\sin 2x[/tex]We need to find its integral
[tex]\int \sin 2xdx=[/tex]Since the integral of sin2x = -cos2x divided by the d/dx of 2x
[tex]\begin{gathered} \frac{d}{dx}(2x)=2 \\ \int \sin 2xdx=-\frac{cos2x}{2}+C \\ \int \sin 2x=-\frac{1}{2}\cos 2x+C \end{gathered}[/tex]The answer should be C