Need some help with integration

[Viper915]

I put this in here too, since i'm technically in grade 12, even though the problem comes from college level calc. I have the problem and a conversation with a friend uploaded as a txt file, so you can understand it a little easier. we have 2 sets of answers that seem to work, and we can't figure out why it seems to work in two different ways. Please shed some light on this, thanks in advance :)

http://members.shaw.ca/w0lf/CalcProblem6.txt

Edit: Problem solved!