Let f:[a,b]→R be an integrable function and (an)⊂R such that an→0.<spanclass=′latex−bold′>a)</span> If A={m⋅an∣m,n∈N∗}, prove that every open interval of strictly positive real numbers contains elements from A.<spanclass=′latex−bold′>b)</span> If, for any n∈N∗ and for any x,y∈[a,b] with ∣x−y∣=an, the inequality ∫xyf(t)dt≤∣x−y∣ is true, prove that ∫xyf(t)dt≤∣x−y∣,∀x,y∈[a,b]Nicolae Bourbacut