open and closed and bounded interval people 

interval $[0,1]$, is closed interval
can you say such interval $[0,1]$ is bounded or not??
if it is how to show this interval is bounded ?(proof?) 
or interval is not enough to say this is bounded or not 
is only apply to the function $f()$?

thank you 

$[0,1]$ is bounded in $\mathbb R$ because there is a point $0$ in $\mathbb R$ from which the distance to any point in this interval is bounded by $1$.
