$$\int_0^{{\pi \over 2}} {{e^{\sin x}}} \cos x\,xdx$$ 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?

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