$$ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin (x-[x]) d x= $$

Here $[x]$ is the greatest integer function

$$ \int_0^2 x^2(2-x)^5 d x= $$

If $f(x)=\max \left\{x^3-4, x^4-4\right\}$ and $g(x)=\min \left\{x^2, x^3\right\}$, then $\int_{-1}^1(f(x)-g(x)) d x=$

$$ \int_0^1 \frac{2 x+5}{x^2+3 x+2} d x= $$