If I were supposed to evaluate the following Integral
$$ \int _{-\infty}^\infty\int _{-\infty}^\infty \frac{e^{ik(y-x)}}{k^2-m^2}dxdk $$ I would supposedly substitute $y-x$ to $z$, and then integrate over $z$ to get a delta function of $k$ and then set $k$ to zero. $$ \int _{-\infty}^\infty\int _{-\infty}^\infty \frac{-e^{ikz}}{k^2-m^2}dzdk = \int _{-\infty}^\infty \frac{-2\pi\delta(k)}{k^2-m^2}dk =\frac{2\pi}{m^2} $$ My question is this mathematically correct?