The notes you posted have a typo. It should read:
(The notes you posted show , which is wrong, since does not depend on .)
Also, the question you posted does not match the notes you posted. The original question should be asking to prove:
Then, the proof follows by using the FTC parts 1 and 2.
Anyway, you say that you understand the derivative of the LHS. It is the derivative of the RHS that you are having trouble with.
Simply take the derivative and that is . You should know how to take the derivative of the natural logarithm. The derivative of with respect to is zero ( is just a constant since is a constant).
Performing some algebra, you find that the derivative of the LHS and the RHS are the same. So, if you take the antiderivatives, they must differ by at most a constant.