Definition RInt (f : R -> V) (a b : R) := iota (is_RInt f a b).

Lemma RInt_gt_0 (g : R -> R) (a b : R) : (a < b) -> (forall x, a < x < b -> (0 < g x)) -> (forall x, a <= x <= b -> continuous g x) -> 0 < RInt g a b.