Screen damage if determined by Apple to be accidental is not covered by the regular warranty. If you have Applecare Plus you get two accidental damages/incidents for the life of the warranty at reduced cost.
iPhone Repair - Screen Damage [and links to other iPhone repair services] - https://support.apple.com/iphone/repair/screen-damage - includes pricing.
iPhone Service Answer Center - https://support.apple.com/iphone/repair/service - "Learn more about iPhone service options, warranty, and pricing." Repair times.
Genius Bar appointment - Go to https://www.apple.com/retail/geniusbar/ > Get hardware help > iPhone > Repairs & Physical Damage > Screen is cracked > Bring in for Repair --> Sign in with Apple ID
That looks like the screen on my iMac. Maybe a connector broken?