By using the quadratic interpolating spline a new class of the quadrature rules was obtained. Those formulas are modifications of the well known trapezoidal rule. The basic characteristic of those formulas is a free parameter. With appropriate choice of that parameter, accuracy of the trapezoidal rule can be improved up to $O(h^4).$ Besides this, by using this nonstandard techniques some well known quadrature rules were also obtained.   2000 Mathematics Subject Classification. 65D32, 65D07

In this paper we describe five methods for the calculation of the moments\begin{equation*}\label{Momenti}\mathbb{M}_{n,m}=\int_{0}^{m}\varphi_{m}(t)t^{n}dt,n\in\mathbb{N}_{0},\end{equation*}where weight function $\varphi_{m}(\cdot)$ is the cardinal B-spline of order $m,m\in\mathbb{N}.$   2000 Mathematics Subject Classification. 65D07, 41A15

Abstract We are considering the quadrature formulas of “practical type” (with five knots) for approximate computation of integral [xxx] where w(·) denotes (even) Tchebychev weight function. We prove that algebraic degree of exactness of those formulas can not be greater than five. We also determined some admissible nodes and compared proposed formula with some other quadrature formulas.