$R$ is integral domain 
Let$ S$ be a subring of$ R$. If $R$ is an integral domain, then $1_R$ = $1_S$?

I know that if $S$ is subring of $R$ then  $S$ is integral domain. How to prove this problem ?
Thanks in advance.

Observe that
$1_S(1_R - 1_S) = 1_S 1_R - 1_S^2 = 1_S - 1_S^2 = 1_S - 1_S = 0; \tag 1$
then since $R$ is an integral domain, if
$1_S \ne 0, \tag 2$
we must have
$1_R - 1_S = 0, \tag 3$
which implies
$1_R = 1_S. \tag 4$
