Section Continuity.
Context {V : NormedModule R_AbsRing}.

Lemma continuous_RInt (f : R -> V) (a b : R) (If : R -> R -> V) :
locally (a,b) (fun z : R * R => is_RInt f (fst z) (snd z) (If (fst z) (snd z)))
-> continuous (fun z : R * R => If (fst z) (snd z)) (a,b).