If Firefox is opened with a URL parameter, the parameter persists through attempts to clear history.
When Firefox is opened with a URL, the URL is a parameter in Firefox's command line and could present a potential privacy leak as it is not cleared by Clear Recent History.
Wšě wotmołwy (1)
In addition, right click on Firefox's launch icon, click "Properties", note the third line; the "COMMAND" entry which most likely reads "Firefox -u". The "-u" is what Anonymous is referring to as a parameter. It (-u) represents an instruction to Firefox to replace your destination URL with another destination that is not intended.
This may point to a virus in an applet, could be a porn site, whatever.
If a pop-up box asks for permission to download a file, DO NOT CLICK OK.
Click "Cancel".
I did a cold boot out of instinct next, then get rid of that "-u". I cannot speak for the clear history but it sounds like a good idea, also. I made sure I had a BACKUP of my bookmarks as a precaution, then did what Anonymous suggested.
Another thought I only have one icon, so cannot vouch for it but you may need to remove the "-u" on each launch Firefox you have.
Also, do not be as blasé as I was, if the URL looks wrong, it probably is wrong. Go browse somewhere else.
Alex