Upper panel: profiles of the emission line from an accretion disc ring extending from 3 to 50 R_S around a Schwarzschild BH (or a slowly rotating NS) with the emissivity radial dependence ∝R⁻². The solid and dashed curves are for the observer inclination of 30° and 60°, respectively. The red curves correspond to the exact treatment of bending. The results using our new approximation given by Eqs. (2) and (17) are shown with the black curves. The blue and green curves correspond to the approximations of Beloborodov (2002) and La Placa et al. (2019), respectively. All of the curves overlap. The pink curves show the profile with no bending accounted for, as in the XSPEC model DISKLINE. The profiles were re-normalised by a factor giving maximum of unity for the exact profile. Bottom panels: relative error in the line flux for the considered approximations.