Whenever you create/recreate the "fun & stress-free" User Profile Service Application in SP2010, you have to create/select an Application Pool in IIS to attach it to.
But what if you want to delete old app pool(s) that you have created & no longer want???
Poweshell has a neat command line to do exactly just that:
Remove-SPServiceApplicationPool <app pool name to be deleted>
You can also use "Get-SPServiceApplicationPool" to show the current ones out there & "New-SPServiceApplicationPool" to create a new one...