4. Determine if each of the following statement is true or false. If it is true, prove it. If it is false, nd a counter example and explain why. (1) Given a function f : [0, 1] > R, if f2 is integrable on [0,1], then f is integrable on [0, 1]. Final Answer This claim is TRUE FALSE. (2) If f,g are integrable on [0,, b] and h is a function such that x) 3 Mm) 3 9(3) for all x 4; [a,b], then h is integrable on [(1,1)]. Final Answer This claim is TRUE FALSE. (3) Assume f is continuous on [a,b] and at) 2 0 on [(1, b]. If Elc E [(1, b] such that f(c) > 0, then fa" f(:r)da: > 0. Final Answer This claim is TRUE FALSE. (4) If f is neither monotone nor continuous on [0,, b], then f is not integrable on [(1,1)]. Final Answer This claim is TRUE FALSE