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 + I₂ ?

$$\int_0^{{\pi \over 2}} {\left| {\sin x - \cos x} \right|} \,dx$$ is equal to

$$\int_0^{{\pi \over 2}} {{e^{\sin x}}} \cos x\,xdx$$ is equal to

Consider the following for the two (02) items that follow:
Let f(x) = [x²] where [.] is the greatest integer function.

What  $\int_{\sqrt{2}}^{\sqrt{3}} f(x) dx$ equal to?