1. Let f(x) =x for a rational x and f(x) =0 for irrational x. (a). Calculate the upper and lower Darboux integrals for f on the interval [0,b] (b). Is f integrable on [0, b] 2. Give an example of a function f on [0,1] that is not integrable for which |f| is integrable . 3. Show that 4. Suppose f is a continuous function on [a,b]. Show that if , then f(x)=0 for all x in [a,b]. 5. Let f and g be integrable functions on [a,b]. Show that max (f,g) and min(f,g) are integrable on [a,b]. \f\f\f\f