In this note, we consider the scattering of s-polarized electromagnetic waves by a cylindrical scatterer lying on the vicinity of a surface separating two homogeneous dielectric media. The scatterer is an inhomogeneous zone of arbitrary shape described by its dielectric constant ε(x,z). The upper and lower media are assumed to have a complex homogeneous, isotropic, linear and local dielectric constant. So far, this problem has received considerably less attention than the corresponding periodic problem. An extensive study using the differential approach has been reported. In this study, an integral equation is used to find the electric field in the inhomogeneous zone. Numerical aspects of the treatment such as evaluation of the Green function will be considered in some detail. From the knowledge of the field within the scatterer, standard calculation gives the far field. Thus, it is possible to compute the diffraction pattern and the extinction cross-section of the scatterer. The numerical results are checked by using the classical criteria of the conservation of energy (optical theorem) and reciprocity. For instance, the relative difference between the total scattered flux and the diminution of the flux in the specular direction is currently less than 10-5; in addition, the reciprocity relations are always verified up to 4 figures.