  Consider the following distribution dependent SDE: $$ {\mathrm d}
X_t=\sigma_t(X_t,\mu_{X_t}){\mathrm d} W_t+b_t(X_t,\mu_{X_t}){\mathrm d} t, $$
where $\mu_{X_t}$ stands for the distribution of $X_t$. In this paper for
non-degenerate $\sigma$, we show the strong well-posedness of the above SDE
under some integrability assumptions in the spatial variable and Lipschitz
continuity in $\mu$ about $b$ and $\sigma$. In particular, we extend the
results of Krylov-R\"ockner \cite{Kr-Ro} to the distribution dependent case.
