Section RInt.
Context {V : CompleteNormedModule R_AbsRing}.
Definition RInt (f : R -> V) (a b : R) := iota (is_RInt f a b).
(** Correction of RInt *)
(* Lemma is_RInt_lim_seq (f : R -> R) (a b : R) : forall If : R, is_RInt f a b If -> is_lim_seq (RInt_val f a b) If. *)
(** ** Usual rewritings *)

Lemma RInt_ext (f g : R -> V) (a b : R) :
(forall x, Rmin a b < x < Rmax a b -> f x = g x) ->
RInt f a b = RInt g a b.