  The present paper is devoted to construction of an optimal quadrature formula
for approximation of Fourier integrals in the Hilbert space $W_2^{(1,0)}[a,b]$
of non-periodic, complex valued functions.
  Here the quadrature sum consists of linear combination of the given function
values on uniform grid. The difference between integral and quadrature sum is
estimated by the norm of the error functional. The optimal quadrature formula
is obtained by minimizing the norm of the error functional with respect to
coefficients. In addition, analytic formulas for optimal coefficients are
obtained using the discrete analogue of the differential operator $d^2/d
x^2-1$. Further, the order of convergence of the optimal quadrature formula is
studied.
