a) Verify that the hypotheses of Fubini's Theorem hold when / is continuous on R.
b) Modify the proof of Remark 12.33 to show that Fubini's Theorem might not hold for a nonintegrable f, even if f(x, y) is continuous in each variable separately; that is, if f(x, ∙) is continuous for each x ∈ [a, b] and f(∙, y) is continuous for each y ∈ [c, d].