We started by reviewing the chain rule. Sometimes he would get mixed up and apply something that looked like the chain rule to the end of an integral.
For indefinite integrals, you add a constant to the end.
The chain rule is very important in many integrals though during the work. Went through some different integrals that used u-substitution and the chain rule. When choosing what is your u, there are usually a few choices. Experience and thinking ahead will help you choose one that works faster.