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The paper is concerned with integrability of the Fourier sine transform function when $f\in {\mathrm{BV}}_0\left(ℝ\right)$, where ${\mathrm{BV}}_0\left(ℝ\right)$ is the space of bounded variation functions vanishing at infinity. It is shown that for the Fourier sine transform function of $f$ to be integrable in the Henstock-Kurzweil sense, it is necessary that $f/x\in L^1\left(ℝ\right)$. We prove that this condition is optimal through the theoretical scope of the Henstock-Kurzweil integration theory.