Operators from $L^{\infty}$ to $L^{\infty}$, below bound of the norm

Question

If $T(f)(x)=\int K(x,y)f(y)dy$, where $K(x,y)$ is locally integrable, is bounded on $L^{\infty}$, how can we show that $\|\int|K(\cdot,y)|dy\|_{L^{\infty}}\le \|T\|_{L^{\infty}\rightarrow L^{\infty}}$?

This problem comes from page 13 of Meyer and Coifman's Wavelets: Calderón-Zygmund and Multilinear Operators.