Definition RInt (f : R -> V) (a b : R) := iota (is_RInt f a b).

Lemma RInt_lt (f g : R -> R) (a b : R) : a < b -> (forall x : R, a <= x <= b ->continuous g x) -> (forall x : R, a <= x <= b ->continuous f x) -> (forall x : R, a < x < b -> f x < g x) -> RInt f a b < RInt g a b.