An equation including the first corrections to scaling for the intensity of small-angle x-ray and neutron scattering from a fluid near its liquid-vapor critical point has been obtained. In the Ornstein-Zernike equation, which, as a number of experiments have verified, is a very good approximation of the inner part of the critical scattering curve, the first corrections to scaling can be made by substitution of expressions for the reduced susceptibility and the long-range correlation length which includes these corrections. (For a one-component fluid, the reduced susceptibility is proportional to the isothermal compressibility.) The amplitude of the corrections to scaling in the Ornstein-Zernike equation has been estimated. One of these corrections was found to have a sign opposite to that determined in an earlier fit of small-angle x-ray-scattering data. This difference may be caused by the fact that previous studies did not consider the slowly changing background scattering from the small-angle tail of the principal maximum of the scattering from the atoms in the fluid.