You can certainly request your US enter-exit records from CBP, however whether or not the information they have is reliable, I don't know. It's my understanding that they enter your name, DOB and other personal information into their database by hand, therefore if they accidently misspell your name (they are all humans after all) there is no guarantee that you get the right responce from them. I wouldn't count on any responce unless I enter my names into the system myself. The reason why I asked them is because I don't personally remember and couldn't locate any records of my ever leaving the country.
My advise to everybody: always be honest with USCIS, because a LIE is the worst crime for them.
Remember that only trips outside the US for 6 month or longer at a time is a material matter. IF they are less then you are still eligible even it you did leave the US. Just list those on your application. You also have to spend more than a half of your total days in the US while being a resident.
I didn't remember taking any trips outside the US, which is why I applied for my exit-entry records from CBP. In fact they only sent my the records for one of my names. They didn't send me anything for my other name used, so I don't know if it means that they just don't have a record, or they forgot to check the other name. I am still waiting for their responce on that.