All of this is a good example of what not to do.
Don't let your parents rule your internet life. I never told my parents what I do my computer because they freak out at the thought of me even having friends. [My mom is crazy, she thinks everyone is a rapist/out to get me LOL.] Not to mention she's very religious, she would throw certain toys away because they were "demonic".
My parents are the same, but I try to hide my history, I never go on anything bad but I don't want my parents freaking out because I watched ''RayWilliamJohnson'' on Youtube.
But like everyone else, some parents are more protective than others, and I'm sure that in their own way, they want to protect you from the internet, just tell them that no matter where you go on the internet or in real life, you will meet bad people, and tell them how you never give personal information out online, it helps with my parents.
Also, delete your history, sometimes it helps, since overprotective parents constantly go, ''whats this and whats that?'' I hightly doubt you'll be watching pornography. X3
But if their decision is final, learn to accept it.