1. Let f : [a, b] -> R be an integrable function. Let ce [a, b] and de R, and let g : [a, b] - R be defined by g(x) = Jf(x) ifre [a, b,x / c if r = C. (a) Prove that g is integrable on R and Jog = Sef. (b) Assuming just that f is bounded (rather than integrable), does it follow that J.g = Jof and g = [ f? Prove your answer correct