The fundamental theorems of Integral Calculus

The fundamental theorems of Integral Calculus

Theorem 2.1 First fundamental theorem of Integral Calculus:

If f (x) is a continuous function and F ( x) = ∫^x_a f (t)dt, then F ′ ( x) = f (x).

Theorem 2.2 Second fundamental theorem of Integral Calculus:

Let f (x) be a continuous function on [a,b], if F ( x) is anti derivative of f (x) , then

∫^b_a f (x)dx = F (b) − F (a).

Here a and b are known as the lower limit and upper limit of the definite integral.