Integrability of trigonometric series with coefficients from the class K

In this paper we deal with a class of sine and cosine trigonometric series. We have imposed some conditions on their coefficients so that their sums will be integrable with the exception of two points. In fact, some estimates of the integrals of the absolute values of their sums, expressed in terms of the coefficients, are obtain extending some results of a paper Telyakovskii, S. A., Localizing the conditions of integrability of trigonometric series, Trudy Mat. Inst. Steklov., 210 (1995), 264–273 (Russian).