Record C1_fun : Type := mkC1
{c1 :> R -> R; diff0 : derivable c1; cont1 : continuity (derive c1 diff0)}.

(* RiemannInt *)
Lemma RiemannInt_const_bound :
forall f a b l u (h : Riemann_integrable f a b), a <= b ->
(forall x, a < x < b -> l <= f x <= u) ->
l * (b - a) <= RiemannInt h <= u * (b - a).