Then 
( )
x
∫a f x dx
 represents the Area function A (x) This concept of area function leads to the Fundamental Theorems of Integral
Calculus � First fundamental theorem of integral calculus
Let the area function be defined by A(x) = 
( )
x
∫a f x dx
 for all x ≥ a, where
the function f is assumed to be continuous on [a, b] Then A′(x) = f (x) for all
x ∈ [a, b]