Lemma ex_RInt_locally {V : CompleteNormedModule R_AbsRing} (f : R -> V) (a b : R) : ex_RInt f a b -> (exists eps : posreal, ex_RInt f (a - eps) (a + eps)) -> (exists eps : posreal, ex_RInt f (b - eps) (b + eps)) -> locally (a,b) (fun z : R * R => ex_RInt f (fst z) (snd z)).