theorem extracted_formal_statement_42.{u_1} {Ω : Type u_1} {m : MeasurableSpace Ω} {μ : Measure Ω}
  [inst : IsFiniteMeasure μ] (a b : ℝ) {X : Ω → ℝ} (hX : AEMeasurable X μ) (h : ∀ᵐ (ω : Ω) ∂μ, X ω ∈ Set.Icc a b) :
  Integrable (fun x => |X x|) μ := sorry

State before:
case bound_integrable.hg
Ω : Type u_1
m : MeasurableSpace Ω
μ : Measure Ω
inst✝ : IsFiniteMeasure μ
t a b : ℝ
X : Ω → ℝ
hX : AEMeasurable X μ
h : ∀ᵐ (ω : Ω) ∂μ, X ω ∈ Set.Icc a b
c : ℝ := ‖a‖ ⊔ ‖b‖
e : ℝ → Ω → ℝ := fun t ω => rexp (t * X ω)
e' : ℝ → Ω → ℝ := fun t ω => rexp (t * X ω) * X ω
⊢ Integrable (fun x => |X x|) μ

Tactic: exact MeasureTheory.Integrable.abs (integrable_bounded a b hX h)

State after:

Relevant lemmas:
MeasureTheory.Integrable.abs : ∀ {α : Type u_1} {m : MeasurableSpace α} {μ : Measure α} {β : Type u_6}
  [inst : NormedLatticeAddCommGroup β] {f : α → β}, Integrable f μ → Integrable (fun a => |f a|) μ