Definition is_RInt (f : R -> V) (a b : R) (If : V) :=
  filterlim (fun ptd => scal (sign (b-a)) (Riemann_sum f ptd)) (Riemann_fine a b) (locally If).Definition ex_RInt (f : R -> V) (a b : R) :=
  exists If : V, is_RInt f a b If.

Lemma ex_RInt_ub (f : R -> V) (a b : R) : ex_RInt f a b -> exists M : R, forall t : R, Rmin a b <= t <= Rmax a b -> norm (f t) <= M.