Abstract
The current article obtains new versions of Ostrowski's type integral inequality by implementing proposed general form of 3-step quadratic kernel. We investigate the new Ostrowski's type integral inequalities for differentiable mapping f with second derivative belongs to two different Lebesgue spaces, namely, f '' is an element of L-1 and f '' is an element of L-2. Moreover, we take into account the case when f '' is an element of L-2. Applications to cumulative distribution function, and to composite quadrature rules are also given.