Well many teens struggle with that kind of stuff and I believe you should get his dad to talk to him about it. Don't get mad at him but just let him know that it's not good to do it and that many kids have them issues. :)
If you think he's doing something he shouldn't, ask him about it. Do not check the history. The more rules you have, the stricter you are, the bigger problem he's gonna be. This comin' from a teenager.
I am a father of three. at any age, do not give me a reason, I will dress them down. Its only to be safe and keep them on track. never not let your children think you are doing the check up out of anger. Or even letting them ride is never a good idea. They Need You ! My children know that every breath is for them. I am not here to get them into trouble. I love each and every single child. My wife and I have done well with our children. they are growing into good people. THERE IS NO PLACE LIKE HOME.
If you are the owner of the account he uses (if you pay the bill for it), most service providers will let you view the phone's history on their website. You can do this on a PC or another phone, without needing physical access to his phone. Whether it is wise to do this is your decision.
I'm not sure what the circumstances are that have made you feel the need to check into his history but, if you need to you can alway contact your Internet provider. As a parent I know that all we want is to keep our kids safe.
First you should ask him what he does on his phone ..... if he tells you then leave him alone, don't go through his stuff because it'll only make him want to hide stuff from you even more, take it from me im 17, plus he needs his privacy just like you need yours.
The question is, why would you want to? I bet he/she doesnt look through your history/data. So why should you do the same? If you do look through it and find something you don't like then it is entirely your fault. As long as he/she isn't affected by what they view on the internet you have no reason to "protect" them. This is coming from an adult.