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_Chasles_1 {V : CompleteNormedModule R_AbsRing} (f : R -> V) (a b c : R) : a <= b <= c -> ex_RInt f a c -> ex_RInt f a b.