You will find them in the following order of battle in the Army of the Mississipi under Rosecrans as an unattached unit:
http://civilwarorderofbattle.com/corinth/union.php
You will find a breif history of the unit during the war here:
http://www.civilwararchive.com/Unreghst/unrginf1.htm#1stinf
If you go here:
http://cdl.library.cornell.edu/moa/browse.monographs/waro.html and look under Series I, Volume XVII, Part I, page 247, you will find a report by Captain George A. Williams on the units' actions during the battle.