Section Derive'.
Context {V : CompleteNormedModule R_AbsRing}.
End Derive'.

Lemma RInt_Derive (f : R -> R) (a b : R):
(forall x, Rmin a b <= x <= Rmax a b -> ex_derive f x) ->
(forall x, Rmin a b <= x <= Rmax a b -> continuous (Derive f) x) ->
RInt (Derive f) a b = f b - f a.