(** * Newton integration *)

Lemma fn_eq_Derive_eq: forall f g a b,
continuity_pt f a -> continuity_pt f b ->
continuity_pt g a -> continuity_pt g b ->
(forall x, a < x < b -> ex_derive f x) ->
(forall x, a < x < b -> ex_derive g x) ->
(forall x, a < x < b -> Derive f x = Derive g x) ->
exists C, forall x, a <= x <= b -> f x = g x + C.