Let $L_2^{(m)}[a,b]$ be the Sobolev space of complex-valued functions defined on the interval $[a,b]$, which possess an absolutely continuous $(m-1)$-th derivative on $[a,b]$, and whose $m$@-th order derivative is square integrable. In this interesting paper, the authors construct and study optimal quadrature formulas in $L_2^{(m)}[a,b]$ in the sense of Sard for numerical integration of highly oscillating integrals, $$ \int_a^b{\rm e}^{2\pi{\rm i}\omega x}\varphi(x){\rm d}x\approx\sum_{\beta=0}^N C_\beta\varphi(x_\beta), $$ where ${\omega\in\Bbb{R}}$. \par Using the discrete analogue of the differential operator $\frac{{\rm d}^{2m}}{{\rm d}x^{2m}}$, they obtain the explicit formulas for optimal coefficients $C_\beta$. The order of convergence of such an optimal quadrature formula is $O(h^m)$. As an application, the authors implement the filtered back-projection (FBP) algorithm, which is a well-known image reconstruction algorithm for computed tomography (CT). By approximating (forward and inverse) Fourier transforms using the obtained optimal quadrature formula for $m=2$ and $m=3$, they observe improved accuracy for the reconstruction algorithm. \par In numerical experiments, they compare the quality of the reconstructed image obtained by using their optimal quadrature formulas with the conventional FBP, in which fast Fourier transform is used for the calculation of Fourier transform and its inversion. In the noise test, it is interesting that the proposed algorithm provides more reliable results against the noise than the conventional FBP.