#### To determine

**To explain:**

Exact meaning of the given statement

#### Answer

The given statement is a colloquial way of stating the fundamental theorem of calculus.

#### Explanation

Compare the given statement to the Fundamental Theorem of Calculus.

Fundamental theorem of calculus: Suppose f is continuous on [a, b] then

1. If gx=∫axf(t)dt then g'x=f(x)

2. ∫abf(x)dx=Fb-F(a), where F is any antiderivative of f, that is, F'=f

From Part 1)

gx=∫axf(t)dt

By takingthederivative of both sides

g'x=ddx∫axf(t)dt

But g'x=f(x), therefore it becomes

fx=ddx∫axf(t)dt

Rearranging the sides

ddx∫axf(t)dt=f(x)

This shows that if we integrate and then differentiate the function, we get the function. In other words, differentiation and integration are inverse processes.

From Part 2)

∫abf(x)dx=Fb-F(a), where F is antiderivative of f, that is F'=f

Replace f by F' on left side

∫abF'(x)dx=Fb-F(a)

It shows that if we integrate the derivative of a function, then the result is the original functionwhich is again the same as the given statement that differentiation and integration are inverse processes.

**Conclusion:**

The given statement is a restatement of Fundamental Theorem of Calculus.