The Fundamental theorem of calculus is a theorem at the core of calculus, linking the concept of the derivative with that of the integral. It is split into two parts. The first fundamental theorem of calculus states that given the continuous function , if Then The second fundamental theorem of calculus states that: The fundamental theorem of calculus has great bearing on practically calculating definite integrals (by taking the antiderivative), unlike other formal definitions such as the Riemann sum.