er-example (if false).
(a) If |f | is integrable on [a, b], then f is also integrable on [a, b].
(b) If f = F ′ for some function F on [a, b], then f is continuous on [a, b].
(c) If g is continuous on [a,b], then g = G′ for some G on [a,b].
(d) If G(x) = ???? x g is differentiable at p ∈ (a, b), then g is continuous at p.