i don't think Apple will accept a broken phone. Best bet is to sell it on Kijiji or eBay, or craigs list if that the popular local ad
If you want most fair value, eBay is the way to go....people will bid on it and determine fair price
if you want to sell it ASAP then do the locals
If you take it to Apple, they might just recycle it for free. I remember back in the day I had a 5 with a small crack on the display as they didn't accept it as a trade in towards a 5s. So I sold it privately on kijiji and it worked out as I got more than their trade in value for a non-cracked 5 any way.
If you want most bang for your buck, trading a phone in is seldom the most bang for your buck whether it is broken or not.
Gazelle will buy broken phones I looked up a quote for a broken 64 GB 6s that powers on and they offered 85 dollars vs 220 for one in good condition
I just sent in a 6 Plus that I broke the screen on and the Touch ID button when trying to fix it instead of waiting for eye surgery and trying to fix it after. They offered 60 but ended up paying 65 bucks.