To remove the items from the address bar (assuming you're using microsoft windows and internet explorer).....
Click on START then SETTINGS move to TASK BAR & START MENU, now fom the properties window that appears click on ADVANCED you'll see a little recycle bin option that says something like....."To remove records of recently accessed documents, programs and web sites, click Clear" if you now click the CLEAR button to the right all the sites in the address bar will be gone.

Few more tips for you from internet explorer goto TOOLS then INTERNET OPTIONS. from here you can set a few options to limit what information is saved. First set the number of days history is saved to 0. Now click on the ADVANCED tab (top right of the properties window) scroll all the way down the list 'til you get to security and check the following option "Empty temp internet files folder when browser is closed".

Hope that helps.......if you have any problems drop me a PM.

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