  It is proved that interval quadrature formula of the form $$
q(f)=\sum\limits_{k=1}^nc_k\frac 1{2h}\int\limits_{x_k-h}^{x_k+h}f(t)dt $$
($c_k\in \RR, \, x_1+h<x_2-h<x_2+h<...<x_n-h<x_n+h<x_1+2\pi -h$) with equal
$c_k$ and equidistant $x_k$ is optimal among all such formulas for the class
$K*F_1$ of convolutions of a $CVD$-kernel $K$ with functions from the unite
ball of the space $L_1$ of $2\pi$-periodic integrable functions.
