End RInt.
(** ** Order *)

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.