tikzpicture add curved arrow in INTERVAL

I am currently working on a slide in which I need to add a curved arrow in the interval as below

Pardon my poor drawing skill in MS paint…

This is my current attempt

    draw[->, thick] (-0.1,0) -- (1.1,0);\

    foreach x/xtext in {0/0,1/1}

    draw[thick] (x,0.5pt) -- (x,-0.5pt) node[below] {xtext};

    draw[bend right=90, ultra thick, blue] (0,0.1) -- (1,0.1);

I researched and found bend might work, but it does not work in the interval (only works for node)

Any suggestions would be appreciated!