I use to work for supercuts and got fired for being late. Can another company find out I got fired?

Anonymous
I worked at super cuts Aug.08-Aug.09. I got fired because I was always late. I am currently applying at different jobs (home depot, star bucks, whole foods, etc.) and want to know if they know that I got fired from super cuts? I didn't put super cuts in my application when I applied to different places. Am I doing wrong? I have changed since then, and never arrive late to my current job. I just think writing down that I got fired on a application will lower my chances of getting a job, so why write it down. Am I doing wrong? What would you do?
I use to work for supercuts and got fired for being late. Can another company find out I got fired?
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