Q:

After upgrading to 2.5: Table 'alpineductless-craft.craft_elementindexsettings' doesn't exist

A client upgraded their site to 2.5, and I believe the update didn't finish.
At first there was a 500 error. I tried rolling the app back (code only) and it  gave an error that the database version didn't support rolling back. Replacing the craft/app directory with a fresh version of 2.5 fixed the 500 error.
The site and some of the admin area work, but in the control panel I cannot access Assets or Entries, I get this error:
CDbCommand failed to execute the SQL statement: SQLSTATE[42S02]: Base table or view not found: 1146 Table 'mysite.craft_elementindexsettings' doesn't exist
So it seems like something with the migration failed. Except must have not been fully failed, because of the error I got about the database version.
The catch is that the client didn't do a database backup before initiating the update, so there isn't a good rollback point. 
Could I manually add this table? Any other potentially fixes for this? Is there a way to tell Craft to re-run the migration to 2.5?

A:

As Lindsey D pointed out in the comment, the answer was to restore the database backup from the automatic backup located in /craft/storage/backups that is generated when the update was initiated.
When this backup is put into place it will re-run the database migration when you visit the Admin area.
So my full solution was 2 steps: 

Replace /craft/app with a fresh copy
Restore the automatically backed up database in /craft/storage/backups

