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In this paper in the space $L_2^{(m)}(0,1)$ the problem of construction ofoptimal quadrature formulas is considered. Here the quadrature sum consists onvalues of integrand at nodes and values of first derivative of integrand at theend points of integration interval. The optimal coefficients are found and normof the error functional is calculated for arbitrary fixed $N$ and for any$m\geq 2$. It is shown that when $m=2$ and $m=3$ the Euler-Maclaurin quadratureformula is optimal.

On an optimal quadrature formula in Sobolev space $L_2^{(m)} (0,1)$