dbcc checkindex runs the same checks as dbcc checktable, but only on the specified index instead of the entire table.
partition_name is the name of the partition you are checking and partition_id is the ID of the partition you are checking. bottom_up specifies that checkindex checks from the bottom up, starting at the leaf of the index. bottom_up is only applicable for dataonly locked tables. If you specify this option with checkindex or checktable, the index checking is done in a bottom-up fashion