Econ Math Proof involving integrals

The proof is: “The derivative of consumer surplus is negative the demand.” P* and Q* = equilibrium price and quantity and Q=F(P) is the demand function Part a) asks to write the CS integral using the inverse demand function F-1(Q), so the integral (0,Q) of (F-1(Q)-P)dQ Part b) says to substitute Q=F(P) for the inverse demand function. This is where I get stuck. Does it become int (P-P*)dQ? dP? After finding this I'm supposed to be able to integrate by parts and get the answer. Any help would be greatly appreciated.