If f is bounded by M on [a, b] and if the restriction of f to every interval [c, b] where c ∈ [a, b] is Riemann integrable, show that f ∈ R[a, b] and that ∫bc f → ∫ba f as c → a+. [Let ac(x) := -M and vc(x) := M for x ∈ [a, c] and ac(x) := ωc(x) := f(x) for x ∈ [c, b]. Apply the Squeeze Theorem 7.2.3 for c sufficiently near a.]