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

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).