Finding derivative with integral 
Came to this problem on my test study guide. I thought for finding the derivative you just took the antiderivative, which would be -cos(theta). How is it sin(x)? Or did I come across another error? At this point In this class I never know anymore. 

$$g(x)=\int_\pi^x\sin\theta\,d\theta=-\cos x+\cos\pi=-\cos (x)-1$$then
$$g'(x)=[-\cos (x)-1]'=\sin x$$
