intros f g a b fg rif eps; destruct (rif eps) as [phi [psi [P1 P2]]].
exists phi; exists psi;split;[ | assumption ].
intros t intt; rewrite <- fg;[ | assumption].
apply P1; assumption.
Qed.
(**********)
Definition RiemannInt (f:R -> R) (a b:R) (pr:Riemann_integrable f a b) : R :=
let (a,_) := RiemannInt_exists pr RinvN RinvN_cv in a.

(* Specifications: *)
Lemma RiemannInt_P5 :
forall (f:R -> R) (a b:R) (pr1 pr2:Riemann_integrable f a b),
RiemannInt pr1 = RiemannInt pr2.