Solution
= Solution
\b[Yes.] <Fubini's theorem> and the triangle inequality give
$$
\begin{aligned}
d_1(Tf,Tg)
&\leq\int_0^1\int_0^1
|K(x,y)|\,|f(y)-g(y)|\,dy\,dx\\
&\leq\|K\|_\infty d_1(f,g).
\end{aligned}
$$
\b[Thus $T$ is Lipschitz continuous with respect to $d_1$ as well.]