How to update my IOS from a Jailbroken Iphone 6S?

Haven't been updating my IOS or Cydia so now I'm out dated. Jailbroke my phone with a IOS version of 9.0.2 now there's 10s out there. Tried updating my IOS to 10ish but my back up says my phone is corrupt when saving it. Was gonna back up my phone and do the update then jailbreak it again.

My dilemma, how do I back up my phone so when I sync it again all my photos and info are saved and primed to sync over when i do update my IOS since updating my IOS will delete Cydia? This corrupt files while backing up my iphone is screwing me over.

Thank you in advance.