∀ {a b : ℝ} {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {f f' : ℝ → ℝ} {g : ℝ → E},
  (∀ x ∈ Set.uIcc a b, HasDerivAt f (f' x) x) →
    ContinuousOn f' (Set.uIcc a b) → Continuous g → ∫ (x : ℝ) in a..b, f' x • (g ∘ f) x = ∫ (x : ℝ) in f a..f b, g x