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I am wondering if anyone knows how schools analyze an applicant's GPA. I had an awful freshman year of college, transferred to a different school, and raised my GPA significantly. Unfortunately, that first year is still factored into my cumulative GPA, as I'm sure you all know. But do schools just look at that number or is there any chance take into consideration the fact that I drastically improved my grades?

It's called an upward trend, and yes it's seen but it's so common that it's difficult for it to be too helpful.

If you have a good reason for the low grades freshman year and you write a compelling addendum, your upward grade trend would likely be looked at more favorably than someone who has similar grade trends because they dicked around and went to class drunk (or whatever) or who has a downward grade trend. But at the end of the day, your cummulative GPA is what the schools have to report, so that's what they're going to see. At best, an upward trend and/or GPA addendum could give you a slight boost in the event of a tie between you and another similarly qualified applicant.