Consider the following for the next three (03) items that follow :

Let f(x) = $\left|\begin{array}{ccc} \cos x & x & 1 \\ 2 \sin x & x^2 & 2 x \\ \tan x & x & 1 \end{array}\right|$

Consider the following for the next two (02) items that follow :

Let f(x) = sin[π²]x + cos[-π²]x where [.] is a greatest ‘integer function

Consider the following for the next two (02) items that follow :

Let f(x) = sin[π²]x + cos[-π²]x where [.] is a greatest ‘integer function

Consider the following for the next three (03) items that follow :

Let $I_1=\int_0^\pi \frac{x}{1+\cos ^2 x} d x$ and 

$I_2=\int_0^\pi \frac{1}{1+\sin ^2 x} d x $