  In this paper, we proved two results regarding the arithmetics of separably
$\mathbb{A}^1$-connected varieties of rank one. First we proved over a large
field, there is an $\mathbb{A}^1$-curve through any rational point of the
boundary, if the boundary divisor is smooth and separably rationally connected.
Secondly, we generalize a theorem of Hassett-Tschinkel for the Zariski density
of integral points over function fields of curves.
