#### To determine

**(a)**

**To explain:**

The meaning of the indefinite integral *∫f(x)dx*

#### Answer

Antiderivative of *f*

#### Explanation

The notation *∫f(x)dx* is traditionally used for an antiderivative of *f*. Thus

*∫f(x)dx=F(x)* means *F'x=f(x)*

**Conclusion:**

Therefore,

*∫f(x)dx* means an antiderivative of *f*

#### To determine

**(b)**

**To explain:**

The connection between the definite integral *∫abf(x)dx* and indefinite integral *∫f(x)dx*

#### Answer

*∫abf(x)dx=∫fxdxab*

#### Explanation

**1) Concept:**

By using Part 2 ofthe fundamental theorem of calculus

**2) Theorem:**

If *f* is continuous on *[a, b]*, then

*∫abf(x)dx=Fb-F(a)*

Where *F* is any antiderivative of *f*, that is, a function *f* such that *F'=f*

**3) Calculation:**

A definite integral *∫abf(x)dx* is a number whereas an indefinite integral *∫f(x)dx* is a function.

The connection between the definite and indefinite integral is given by part 2 of the fundamental theorem

If *f* is continuous on *[a, b]*, then

*∫abf(x)dx=∫fxdxab*

**Conclusion:**

Therefore,

*∫abf(x)dx=∫fxdxab*