Primitive function

1003107804

Level: 
B
Four girls evaluated the integral I=sinxcosxdx on R. Ann started to integrate by parts like this: I=sinxcosxdx=sin2xcosxsinxdx. Beth started to integrate by parts like this: I=sinxcosxdx=cos2xsinxcosxdx. Claire used substitution a=sinx like this: I=sinxcosxdx=ada. Diana integrated sinxcosxdx=cosxsinx+c, cR. Which of the girls made a mistake?
Diana
Ann
Beth
Claire