Step 1:

The integral is .

Symmetry property of integrals: If is an even function then , .

And if is an odd function then , .

Here the integrand function is  .

Replace in the above function.

Thus, the function is odd function.

Therefore, .

The statement is true

Step 2:

(b)

The integral is .

Symmetry property of integrals: If is an even function then , .

And if is an odd function then , .

Here, the integrand function is .

Replace in the above function.

Thus, the function is an even function.

Therefore, by the symmetry properties of integrals,

.

The statement is true.

Step 3: 

The integral is .

Rewrite the integral as .

Determine the integral by using by integration parts.

Integration by parts: .

.

Therefore, .

The statement is false.

Step 4:

(d) The integral is .

Power rule of integration:.

.

Therefore, .

The statement is false.

Solution:

(a)

The statement is true.

(b)

The statement is true.

(c)

The statement is false

(d)

The statement is false