Record C1_fun : Type := mkC1
{c1 :> R -> R; diff0 : derivable c1; cont1 : continuity (derive c1 diff0)}.

Lemma RiemannInt_P33 :
forall (f:C1_fun) (a b:R) (pr:Riemann_integrable (derive f (diff0 f)) a b),
a <= b -> RiemannInt pr = f b - f a.