Fall Out Boy are a American Rock Band which first started in 2001.
Patrick Stump, Guitarist and Vocalist founded the band in 2001, Pete Wentz bassist, Joe Trohman Guitarist and Andy Hurley Dummer all joined the group from different bands.
Their first album was 'Evening without your girlfriend'.
http://en.wikipedia.org/wiki/Fall_Out_Boy's_Evening_Out_with_Your_Girlfriend

Here are some links:
http://www.youtube.com/results?search_query=fall+out+boy+i+don%27t+care&oq=fall+&gs_l=youtube.1.0.35i39l2j0l8.73498.75125.0.76021.5.5.0.0.0.0.118.488.3j2.5.0...0.0...1ac.1.11.youtube.z-Aqx0hfsdc

http://www.youtube.com/results?search_query=fall+out+boy+&oq=fall+out+boy+&gs_l=youtube.3..35i39j0l9.256972.259220.0.259509.12.12.0.0.0.0.505.1657.2j8j5-1.11.0...0.0...1ac.1.11.youtube.5RuaRIxLzVM