MVT for Integrals, 1st FTC, and 2nd FTC Proofs Section 4.4 is chock full of gold. There is a lot there, so the video lets you take it in.

Here are the Subjects by Time:

0:00 - The MVT for integrals (Average Value Thm) & AVERAGE VALUEs

4:20 - An example with f(x) =6 and a curious observation

6:24 -The First Fundamental Theorem Proof

11:16 - An Example of FTC1

12:51 - "Net Change Theorem" version of FTC1 with a "word problem" example

15:27 -The Second Fundamental Theorem of Calculus with for examples

19:05 - The End