So I'm reading my lecturer's notes on Gauss-Chebyshev Quadrature (lecturer uses the word Formulation instead of Quadrature) and there is a point where he lost me completely.

Here are his notes and the points which confuse me:

I understand he substituted $\space x= \cos{\theta} \space$, but my issue is in the integral I circled.

How does is the numerator become $\space f \left( \cos{\theta} \right) \sin{\theta} d\theta \space$ ?

Where did the $\space \sin \theta \space$ come from?

${dx \over d \theta} = -\sin \theta$
$dx = -\sin \theta d \theta$