26D15.

We give some further answers to the open problem posed in the article [Feng Qi, Several integral inequalities, J. Inequal. Pure and Appl. Math., 1(2) (2000), Art. 19.] Being Qi's inequality of moment type, we consider the moments of uniformly distributed random variables and construct certain suitable probability measures to solve the posed problem. Moreover, reverse inequality to Qi's and other related results are deduced as well.