If $I_{1}=\int _{e}^{e^{2}}\frac{dx}{ln~x}$ and  $I_{2}=\int _{1}^{2}\frac{e^{x}}{x}dx$  then which one of the following is correct?

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?

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

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

Direction : Consider the following for the items that follow :

Let f(x) = |x² - x - 2|

What is $\rm \int_0^2f(x)dx$ equal to