People make life difficult on themselves. This stuff is published in plain English on the website for each of the two carriers. Why not check there?

Answer could not be more clear: $25 for first bag. End of story.

United
http://www.united.com/CMS/en-US/trav...edBaggage.aspx

American
http://www.aa.com/i18n/travelInforma...e.jsp#!charges