(* Lemma RInt_comp_opp (f : R -> V) (a b : R) : ex_RInt f (-a) (-b) -> RInt (fun y => f (- y)) a b = opp (RInt f (-a) (-b)). *)

Lemma RInt_plus :
forall f g a b, ex_RInt f a b -> ex_RInt g a b ->
RInt (fun x => plus (f x) (g x)) a b = plus (RInt f a b) (RInt g a b).