Given $t \in \mathbb{R}$ and $z = x + iy$ and $y>0$. $\lim_{y\to0^+} \frac{1}{t - z} = \frac{1}{t-x} + \pi i \delta(t-x)$
This limit is given in the book Integral Transforms and Their Applications - Debnath 2nd ed. (pg 379)
I don't understand how this limit was evaluated. Please help out.