Any useful screen recorder (ios9.1, so not jailbroken)

That's becasue there is simply no option.

The easiest (for certain definitions of "easy") way to record an iOS device's screen on a non-jailbroken device is to install AirServer or a similar piece of software on a computer, ensure both iOS device and computer are on the same network, and then just use AirPlay to cast to the computer. AirServer can record the cast, or you can use normal screen-recording software on the computer.

(A similar trick works with a stock Android device; ChromeCatch or a similar tool to receive a Chromecast-mirrored screen, etc.)

Of course, the downside is that "have your mobile device and an actual computer on the same network" is not always so easy when out in the open in a park or something. :/