Best quadrature formula on the class $W_*^rL_2$

For the classes of periodic functions with $r$-th derivative integrable in the mean,we obtain a best quadrature formula of the form
$$\begin{gather*} \int_0^1f(x)\,dx=\sum_{k=0}^{m-1}\sum_{l=0}^{\rho}p_{k,l}f^{(l)}(x_k)+R(f),\quad0\le\rho\le r-1, \\ 0\le x_0<x_1<\dots<x_m-1\le1, \end{gather*}$$
where $\rho=r-2$ and $r-3$, $r=3,5,7,\dots$, and we determine an exact bound for the error of this formula.