∀ {a b : ℝ} {f f' g : ℝ → ℝ},
  ContinuousOn f (Set.uIcc a b) →
    (∀ x ∈ Set.Ioo (min a b) (max a b), HasDerivWithinAt f (f' x) (Set.Ioi x) x) →
      ContinuousOn f' (Set.uIcc a b) →
        ContinuousOn g (f '' Set.uIcc a b) → ∫ (x : ℝ) in a..b, (g ∘ f) x * f' x = ∫ (u : ℝ) in f a..f b, g u