For this we have to apply integration by parts

Let u and v be two functions then

To choose the first function u we use “ILATE” rule

That is

I=inverse trigonometric function

L=logarithmic function

A=algebraic function

T=trigonometric functions

E=exponential function

So in this preference, the first function is chosen to make the integration simpler.

Now, In the given question x² is an algebraic function and it is chosen as u(A comes first in “ILATE” rule)

So first let us integrate the equation and then let us substitute the limits in it.

Let us recall a formula cos2x=2–1

Now substitute it

Now let us recall other formula i.e=

and

Using them we can write the equation as

On substituting these values we get