Addition to V. P. Zastavnyi's paper “Estimates for sums of moduli of blocks in trigonometric Fourier series”

Results on the integrability and integrability with power weight for sums of moduli of blocks from the series $\sum1/k\sin kx$ are extended to the class of series $\sum b_k\sin kx$ with coefficients $b_k$ of a more general form.