∀ {ι : Type u_1} {E : Type u_2} {μ : MeasureTheory.Measure ℝ} {l : Filter ι} [l.IsCountablyGenerated]
  [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {a b : ι → ℝ} {f : ℝ → E},
  MeasureTheory.Integrable f μ →
    Filter.Tendsto a l Filter.atBot →
      Filter.Tendsto b l Filter.atTop →
        Filter.Tendsto (fun i => ∫ (x : ℝ) in a i..b i, f x ∂μ) l (nhds (∫ (x : ℝ), f x ∂μ))