My Iphone 4s keeps shutting down?

My Iphone 4s version 5.1.1 keeps shutting down every few minutes and opens with it self, and it happened all day long so i turned it off for few hours and opened it after then but it kept doing the same thing and the battery kept going from 48% to 70% and then after 10% so i waited till the battery dies, but when it came to 1% it made the same thing and turned off without turning on again so i should have saw when it turned off that i need to plug the charger in but i didn't see it so i just plugged the charger in and it went to 100% while opening it so i removed the charger and kept happening all over again… So is there anything i could do to make my phone work normally or know were the problem is?

Added (1). I don't want to update the software because it will delete everything on my Iphone.

Plug it into the computer on iTunes and update it to iOS 6.

Plug it into itunes and press "no" to the option to upgrade to ios 6, then press the button that says "back up to itunes". This will save EVERYTHING on your phone. Then update to ios 6 by pressing "software update" button. After its done complete the steps on the iphone screen, then it will ask if you want to restore through icloud, itunes, or set up as new iphone. Click the itunes option, then on your computer click on "restore from back up" and click on the appropriate one. If the problem persists, call apple and check your apple care status. If your still covered, they will replace your iphone for free

Gurl you take dat thang straight to apple and you tell dem it don't work

I think it must has some thing wrong with your battery, you should take it to Apple store to get fixed.