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 [11,, b] and h is a. function such that f(1:) S Mm) S g(:c) for all a: E [cub], then In is integrable on [(1,5)]. Final Answer This claim is TRUE FALSE. (3) Assume f is continuous on [(1, b] and f(:r:) 2 0 on [a,b]. If Elc e [(1, b] such that f(c) > 0, then f: f(m)da: > 0. Final Answer This claim is TRUE FALSE. (4) If f is neither monotone nor continuous on [a., b], then f is not integrable on [(1, b]. Final Answer This claim is TRUE FALSE