Fundamental theorem of calculus
![The area shaded in red stripes can be estimated as h times f(x). Alternatively, if the function A(x) were known, it could be computed exactly as A(x + h) − A(x). These two values are approximately equal, particularly for small h.](/Images/godic/202501/14/FTC_geometric.svg0933.png")
![](/Images/godic/202501/14/Riemann_integral_irregular0934.gif")
The fundamental theorem of calculus is a theorem that links the concept of the derivative of a function with the concept of the function's integral.
The first part of the theorem, sometimes called the first fundamental theorem of calculus, is that the definite integration of a function is related to its antiderivative, and can be reversed by differentiation. This part of the theorem is also important because it guarantees the existence of antiderivatives for continuous functions.