Fundamental Theorem of Calculus. If we define an area function, F (x), as the area under the curve y=f (t) from t=0 to t=x, then the area function in this case is F (x)=c∗x. We would like to be able to evaluate more integrals with a process like this, The fundamental theorem of calculus tells us that if f is continuous over this interval, then F of x is differentiable at every x in the interval, and the derivative of capital F of x
