Definition is_RInt (f : R -> V) (a b : R) (If : V) :=
  filterlim (fun ptd => scal (sign (b-a)) (Riemann_sum f ptd)) (Riemann_fine a b) (locally If).Definition ex_RInt (f : R -> V) (a b : R) :=
  exists If : V, is_RInt f a b If.

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