intros f a b H.
case (Rle_or_lt a b); intros H1.
apply ex_RInt_Reals_1.
apply continuity_implies_RiemannInt.
exact H1.
intros x _; apply H.
apply ex_RInt_swap.
apply ex_RInt_Reals_1.
apply continuity_implies_RiemannInt.
left; exact H1.
intros x _; apply H.
Qed.

Lemma Iu1: forall a b, ex_RInt (fun u => u1 u) a b.
intros a b.