My ipad air left side upper corner is broken so what to do

You have two choices:

Make an appointment at your local apple store and pay the fee for an out of warranty replacement. For an Air I believe the fee starts at $299 and goes up depending on the model.

Choice 2 is to use a non-authorized repair place. Which may be cheaper, however once you go to a non-authorized repair place your factory warranty will be null and void, so if anything else further goes wrong you're on your own.

Or, I guess choice 3 would be to put a screen protector on it and live with it.

Apple's Limited Warranty http://www.apple.com/legal/warranty/ for iPad excludes coverage for damage resulting from accident, disassembly, unauthorized service and unauthorized modifications.

The warranty will apply to the country of purchase. And if there is a problem needing repair you have to return it to the country of purchase.

Out-of-Warranty Service

If you own an iPad that is ineligible for warranty service but is eligible for Out-of-Warranty (OOW) Service, Apple will replace (Apple doesn't repair) your iPad with an iPad that is new or equivalent to new in both performance and reliability for the Out-of-Warranty Service fee listed below. (The replacement will most likely be a refurbished iPad in a brown box, however, it has a new screen, back and battery.)

A $6.95 shipping fee will be added if service is arranged through Apple and requires shipping. All fees are in US dollars and are subject to local tax.

Certain damage is ineligible for out-of-warranty service, including catastrophic damage, such as the device separating into multiple pieces, and inoperability caused by unauthorized modifications. However, an iPad that has failed due to contact with liquid may be eligible for out-of-warranty service. See http://support.apple.com/kb/index?page=servicefaq&geo=United_States&product=ipad

Make a Genius Bar Reservation

http://www.apple.com/retail/geniusbar/

You may can get the iPad repaired at 3rd party repair sources for less $, however, any remaining Apple warranty will be voided.

iCracked - Broken iPhone, iPod or iPad

http://www.icracked.com/

iReVamp Electronics Screen Repair ($99)

http://www.irevampelectronics.com/ipad-2-broken-glass-screen-repair.html

iPad Repair & Screen Replacement Services

http://www.ifixyouri.com/16-ipad-repairs

RepairZoom iPad Repair

http://www.repairzoom.com/ipad-repair.html

Mission Repair

http://www.missionrepair.com/Apple_iPad_Repair_Services_s/431.htm

iGadgetResQ

http://www.igadgetresq.com/ipad-repair/

Do It Yourself iPad Repair

http://www.ifixit.com/Device/iPad

 Cheers, Tom 😉