(** Addition *)

Lemma RiemannInt_plus : forall (f g : R -> R) (a b : R)
(pr_f : Riemann_integrable f a b) (pr_g : Riemann_integrable g a b)
(pr : Riemann_integrable (fun x => f x + g x) a b),
RiemannInt pr = RiemannInt pr_f + RiemannInt pr_g.