OS X Mavericks :: Safari Opens To Unknown Website?

When I turn on the computer, Safari automatically opens to [URL].... I know nothing about this site. I have, previously, set my Safari/Preferences to open to a different site. That used to work. 

WORSE ... sometimes when turning on the computer, the screen gets stuck on the big wave open background. Only the very top toolbar for Finder opens. But Desktop icons do not appear. And the mouse is inoperable. I have to manually turn off the computer, turn it back on ... and then, sometimes (not sure how consistent this is), it automatically opens to Safari on that Trusteer website (that I have never, to my knowledge, accessed). 

I took this problem once before to this community. Was given instructions to do a Safe Boot, which I did. It was not supposed to fix the problem. But after I did it, the problem seemed to go away... for a while. It's back now. 

I also did a Disk Utility Repair of the HD. 

I have not clicked on anything in that Trusteer page because I don't trust it. It looks legitimate. Is it? 

This problem, by, the way, only began after I upgraded to Mavericks. I don't recall how long it was before the problem started after upgrading. Probably a couple of weeks.