Every time I close Safari the last page viewed 'pops up' on reopening

please help me..

When I close Safari on my brand new MacBook Air, as force of habit because I am not the only one to use my computer, I close Safari and Firefox- first clearing the history.

When I reopen Safari, guess what? The last thing I was looking at AND all my search history (that I THOUGHT that I deleted) is right there, for all to see.

This is impossible! But it is right there... my browsing history.. the last web page I viewed AND all windows that were open in my last session.

What is going on here?

Am I doing something wrong?

I've NEVER had this problem with any of my older macs.. just the new ones and just in Safari..