If I'm seeing it right that is the back of the transmission (most would call it the rear end) and that's one big chuck of metal.
The reason for it's damage is either the bearing failed, teeth on either gear failed or the PTO got overworked and caused the case to fail.
You can get it new P/N K2581-11014 $930.00 or so US
Another option is West Kentucky Tractor Parts,
http://wkytpstore.com/, but be warned there is 3 cases for that model of tractor based on Serial #
All will take the new case but the older cases will not fit it properly.
You can find out the case # by the serial # of the tractor that the case comes out of.
P/N K2581-11012 , Serial # <=57011
P/N K2581-11013 , Serial # >=57012
P/N K2581-11014 , Serial # >=62769
There is also going to be a ton of other seals, gaskets and parts involved with a repair like this.
