It means that the curve \( 1/(k-k_0) \) has equal and opposite areas on both sides of the singular point \( k_0 \). If we break the integral into one over positive \( k \) and one over negative \( k \), a change of variable \( k\rightarrow -k \) allows us to rewrite the last equation as $$ \begin{equation*} \int_{0}^{\infty} \frac{dk}{k^2-k_0^2} =0. \end{equation*} $$