Read the following information carefully and answer the questions given below.

Given that, $${a_n} = \int_0^\pi {{{{{\sin }^2}\{ (n + 1)x\} } \over {\sin 2x}}dx} $$

Consider the following statements

1. The sequence $$\{ {a_{2n}}\} $$ is in AP with common difference zero.

2. The sequence $$\{ {a_{2n + 1}}\} $$ is in AP with common difference zero.

Which of the above statements is/are correct?

Read the following information carefully and answer the questions given below.

Given that, $${a_n} = \int_0^\pi {{{{{\sin }^2}\{ (n + 1)x\} } \over {\sin 2x}}dx} $$

What is $${a_{n - 1}} - {a_{n - 4}}$$ equal to ?

What is $$\int_{ - 2}^2 {x\,dx - \int_{ - 2}^2 {[x]} \,dx} $$ equal to, where [ . ] is the greatest integer function?

If $$\int_{ - 2}^5 {f(x)dx = 4} $$ and $$\int_0^5 {\{ 1 + f(x)\} dx} = 7$$, then what is $$\int_{ - 2}^0 {f(x)dx} $$ equal to ?