Curious

[Social Democratic Confederation]

I'm in a college calculus class (this being my senior year in high school). A few months ago my class was introduced to definite integration. I have a solid handle on that, though the book gave no proof for that kind of integration. All it said was that

 

 

∫f(x) = F( - F(a).

 

 

I know this is true, but the book provided no proof as to how humanity knows that the difference of the antiderivatives of the endpoints is equal to the area under the curve. I wanna know why, but cant find the proof anywhere and my professor is clueless himself as to what the proof is.

 

Anyone else know the proof for definite integration (or your textbook has it), or able to find a site the provides it?

Edited February 16, 2008 by Social Democratic Confederation (see edit history)