What does FTC part 1 says ?
So now, here is what I propose to you : arrange the original integral in order to get a smilar form to what the FTC gives.
(because in the FTC, t is on the upper boundary - and there's a - sign because you inverted the order of boundaries)
Now, what if you let ? You will be able to let t in the upper boundary of the integral. And
Apply FTC :
Apply chain rule in the LHS :
Substitute back :
Does this look clear enough ?