Problem 2 (4 points each) In this problem. we will look at some properties of the Riemann integral of the absolute value of a function. (a) Suppose f E 9? 2?,[a b]. Show that |f| 6 3mm] 15]. and that _/:f| f m (1)) Find an example of a function f : [(5.3)] > JR such that |f| 6 3'4? [(1,3)] but f g a, b]. (Hint: Think about the Dirichlet function) (c) Suppose f : [ca b] > JR is continuous. Show that if f((:) > U for some (2 E [ab] then there exists some 6 > 0 such that c+5 / f > 0 (26 (Remark: Try to be careful about strict / non-strict inequalities and open / closed inter- vals in this part.) ({1} Suppose f : [(1.3)] > IR; is continuous. Show that f|=0 if and only if f(:r) : 0 for all 3*: 6 [ca b]