  In this paper problem of construction of optimal quadrature formulas in
$W_2^{(m,m-1)}(0,1)$ space is considered. Here by using Sobolev's algorithm
when $m=1,2$ we find the optimal coefficients of the quadrature formulas of the
form $$ \int\limits_0^1\phi(x)dx\cong
\sum\limits_{\beta=0}^NC_{\beta}\phi(x_{\beta}). $$
