2. Let f be a bounded function on [a, b]. Prove the following statements. U_{P}(f)-L_{P}(f)<\epsilon_{a} (a) If f is integrable on [a,b], then Ve > 0, there exists a partition P of [a, b] such that ) If Ve > 0), there exists a partition P of [a, b] such that Uµ(ƒ) — Lµ(ƒ) < ¤, then ƒ is integrable on [a, b]. \text { Let } x \in \mathbb{R} . \quad \text { IF } \forall \epsilon>0, x<\epsilon \mathrm{THEN} x \leq 0 .