Let f: [a, b] R be an integrable function. Let g: [a, b] - R be a function which agrees with f at all points in [a, b] except for one, i.e. assume there exists a c [a, b] such that g(x) = f(x) for all x = [a, b] \ {c}. Prove that g is integrable on [a, b] and that S g(x)dx = f f(x)dx.