I tried this integral but Im not sure I got the correct answer. I got cos(1-x)+C
Integral sin(1-x)dx
as nzmathman said, you are correct. you could check for yourself though. if you differentiate you answer, you should get the original integrand. since (by the chain rule) $\displaystyle \frac d{dx}[\cos(1 - x) + C] = \sin (1 - x)$, you are correct
you may also want to check this out