4. Determine if each of the following statement is true or false. If it is true, prove it. If it is false, find a counter example and explain why. \text { (1) Given a function } f:[0,1] \rightarrow \mathbb{R} \text {, if } f^{2} \text { is integrable on }[0,1] \text {, then } f \text { is integrable on }[0,1] \text {. } 2) If f, g are integrable on [a, b] and h is a function such that f(x) ≤ h(x) ≤ g(x) for all z € [a,b],then his integrable on [a, b]. 3) Assume f is continuous on [a, b] and f(x) > 0 on [a, b]. If 3c € [a, b] such that f(c) > 0, then \text { If } f \text { is neither monotone nor continuous on }[a, b] \text {, then } f \text { is not integrable on }[a, b] \text {. } ) (Do not submit) If f is neither monotone nor continuous on every subinterval of [a,b], then fis not integrable on [a, b].