  In the present paper the problem of construction of optimal quadrature
formulas in the sense of Sard in the space $L_2^{(m)}(0,1)$is considered. Here
the quadrature sum consists of values of the integrand at nodes and values of
the first and the third derivatives of the integrand at the end points of the
integration interval. The coefficients of optimal quadrature formulas are found
and the norm of the optimal error functional is calculated for arbitrary
natural number $N$ and for any $m\geq 4$ using S.L. Sobolev method which is
based on discrete analogue of the differential operator $d^{2m}/dx^{2m}$. In
particular, for $m=4,\ 5$ optimality of the classical Euler-Maclaurin
quadrature formula is obtained. Starting from $m=6$ new optimal quadrature
formulas are obtained.
