This tutorial has two more examples for finding area under a curve using the limit definition of a derivative. In these examples, the lower bound is not zero.
Once you are done with these two examples, you should be able to do find the area under any polynomial curve of degree 3 or less.
http://www.hippocampus.org/HippoCampus/Calculus & Advanced Math?loadLeftClass=Course&loadLeftId=136&loadTopicId=9269
Show me at least one completed problem from Stewart #21, 23-25.
This is worth 5 points. If it is not done at the very beginning of class, it's a zero.
Check your final answer. If you make a mistake, you must fix it, and show me where you went wrong and where you found your mistake.