The function is .

Graph the area represented by the above function.

.

Part 1 of the fundamental theorem of calculus :

If  is continuous on , then the function  is defined by  is continuous on  and differentiable on , then .

Compare  with .

The function is .

The derivative of the function :

.

The derivative of the function .

(b)

The function is .

Part 2 of the fundamental theorem of calculus :

If  is continuous on ,.

Where  is any anti derivative of  , that is a function such that .

Anti derivative of the constant function  is .

Anti derivative of the function  is .

Differentiate on each side with respect to .

The derivative of the function .