iPhone broken falling from car
iTunes on your PC can make a backup of your device quite easily - especially if you have the two devices paired before the fall.

If you haven't paired it, you'll need to have at least the digitizer working to tap to trust the computer once.

Once that's done (and iTunes will prompt you), you can use the PC to back up the entire phone and/or choose to synchronize the calendar data with the PC.

Best of luck and you probably could call AppleCare for free to arrange a repair and get help backing it up before he repair starts.