To wipe the history in IE11 and 10, go to the Gear icon at upper left and select Internet Options. On the General tab, you can check a box next to Delete browsing history on exit, or click the Delete button to instantly get rid of history, passwords, cookies, cached data (called Temporary Internet files and website files), and more. If you instead click Settings, you go to a History tab and ensure your history is only collected for a specific number of days, automatically deleting anything older.
You have the option to get rid of your browsing history using the Favorites Menu. Click the star on the top-right > History tab. There, you can see websites you visited on specific dates (Today, Last Week, 3 Weeks Ago, etc.) Right-click to delete everything from a specific time period, or click to view and delete specific websites