How would I construct Schwartz functions $f_1^\epsilon$, $f_2^\epsilon$ on $\mathbb{R}$ such that
$f_1^\epsilon(x)\leq\mathbb{1}_{[a,b]}(x)\leq f_2^\epsilon(x)$,
and $f_1^\epsilon\rightarrow\mathbb{1}_{[a,b]}$, $f_2^\epsilon\rightarrow\mathbb{1}_{[a,b]}$ as $\epsilon\rightarrow0$,
where $a are real numbers and $\mathbb{1}_{[a,b]}$ is the indicator function?