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

Consider the integrals

$$A = \int_0^\pi {{{\sin xdx} \over {\sin x + \cos x}}} $$ and

$$B = \int_0^\pi {{{\sin xdx} \over {\sin x - \cos x}}} $$

Which one of the following is correct?

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

Consider the integrals

$$A = \int_0^\pi {{{\sin xdx} \over {\sin x + \cos x}}} $$ and

$$B = \int_0^\pi {{{\sin xdx} \over {\sin x - \cos x}}} $$

What is the value of B?

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

Consider the integral

$${I_m} = \int_0^\pi {{{\sin 2mx} \over {\sin x}}dx} $$, where m is a positive integer.

What is I₁ equal to ?

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

Consider the integral

$${I_m} = \int_0^\pi {{{\sin 2mx} \over {\sin x}}dx} $$, where m is a positive integer.

What I₂ + I₃ equal to ?