what is the value of $$\int\limits_{ - \pi /4}^{\pi /4} {(\sin x - \tan x)\,dx} $$ ?

If $$\int\limits_a^b {{x^3}} dx = 0$$ and $$\int\limits_a^b {{x^2}} dx = {2 \over 3}$$, then what are the values of a and b respectively ?

What is $$\int\limits_0^1 {x{{(1 - x)}^9}} dx$$ equal to ?

Read the following information and answer the questions given below.

Consider the integrals

$${I_1} = \int_0^\pi {{{xdx} \over {1 + \sin x}}} $$ and

$${I_2} = \int_0^\pi {{{(\pi - x)dx} \over {1 - \sin (\pi + x)}}} $$

What is the value of I₁ ?