Your history is stored in the places.sqlite database and there's no convenient procedure to export or import it. I think you may just want to keep that file, then after installing Firefox afresh, exit out of it, delete the new places.sqlite file and copy the old one into its place. These articles might be useful in that process:

• Profiles - Where Firefox stores your bookmarks, passwords and other user data
• Recover important data from an old profile

The only way to backup history is to copy history items to a bookmarks folder and export them that way.
Firefox only keeps backups of the bookmarks and not of the history.

See also:

• http://www.nirsoft.net/utils/mozilla_history_view.html