Stop looking at the porn...LOL.
JK
I don't know about Firefox, but on IE you simply go to Tools and Delete Browsing History.
Also, you truly do not have privacy on the internet. If you guys have a home network, he could simply log into the router and see the history of ALL the websites you have visited and at what time.
If you want true privacy from your family, you need to buy/rent your own place and then pay for your own internet service. Then, only YOU, the CABLE company and the GOVERNMENT know what websites you have been visiting.