University of California Irvine Darboux Integral Questions Response

please writing clearly or typing if u prefer typing

please solve these 2 questions

thank u

4. (10pts) Let f(x) = x2 if x is rational and 0 otherwise. For b > 0, consider the
upper and lower darboux integrals U(f) and L(f) of f on (0,b].
(a) Find U(f).
(b) Find L(f).
5. (10pts) Show that if f is a continuous function on [0, 0), and lim f(x) = c,
then lim z S* f(t)dt = c.
2->
20