Should he be doing that?

Me and my boyfriend have been dating almost a year now. He is my first for everything and I'm his first as well for everything. I recently found out that he had been looking up girls that he all ready knows, on the internet. I confronted him and he as usual gets his act of I dont care. He said he didnt know why he did it and he turned it around on me and asked why I was invading his space. I have gone through his stuff before and found a picture of the same girls legs on his phone, that he had taken in school. What do I do to stop this? Comments.