I have to ask about this one myself.
After the product rule I have:
I don't see how you would differentiate the integral in the second term with the FTOC because it is indefinite, the FTOC is always stated in terms of definite integrals as far as I understand it. I guess if say that is always true so I can say my is my and just say
Or maybe I shouldn't ask if it is true, it is just definition of integral? Where does chain rule come in?