iOS 9.1 vs iOS 9: What’s New in iOS 9.1

Live Photos Fixes for iPhone 6s and iPhone 6s Plus

Apple includes a fix for Live Photos on the iPhone 6s and iPhone 6s Plus that is designed to prevent the live portion from recording the time you bring the camera up and the time you are brining it down from taking a photo. 

There is some improvement, but it does not completely fix the issue as many users still see Live Photos recording the start or the end of a photo session. You don't need to do anything to try it, just take a Live Photo.