The first fundamental theorem of calculus begins by defining a function like this: http://i.imgur.com/aWXql.png (sorry was not sure how to write this legibly in this post so I just uploaded on imgur) I kind of have a hard time wrapping my mind aruond this. How do you chose a? I feel like in the proof for the fundamental theorem, a ends up canceling out and doesn't matter, but it's hard for me to look at this and see and understand that. If F is an antiderivative of f, then you would end up with F(x)-F(a) isn't it? By the second fundamental theorem? I'm so confused every time I look at this. I just don't understand how a is or is not relevant and how this function is defined this way.