please help me.

Problem 1. Let S be the set of all continuous functions f: [0,1] - IR such that So xf (x)dx =1. Find the minimum value of fox2(1 + x2)(f(x))"dx, where f lies in S. If possible, provide one f in S for which the minimum is attained. Problem 2. Result 1. If p: [a, 00) - IR be monotonic, bounded on [a, co) and limx-.. (x) =0, and the function Sa f (t) dt is bounded on (a, co), then the integral Ja f(t)$(t)dt converges. Result 2. If a function g: [a, b] - IR is continuous on [a, b], then there exists a constant M > 0 such that Ig(x)|