- you substitute, and you change the boundaries
- you substitute, and you don't change the boundaries. In which case, you have to «back substitute», that is : after you got an antiderivative in terms of the new variable, substitute it with the old variable, and keep the limits.
But I think the first one is better, because for the second one, it would be more correct to write :
, so that you know that it's the boundaries for theta.
While for the first situation, you can just say
Got it ?