$\int_2^3 \frac{d x}{x^2-x}$ is equal to

Evaluate $\int_{-2}^1 f(x) dx$,where $f(x) = \begin{cases} 1-2x, & x \leq 0 \\ 1+2x, & x \geq 0 \end{cases}$

$\int_{e^{-1}}^{e^2} \left| \frac{\log x}{x} \right| dx =$

$\int_{-1}^{3/2} |x \sin \pi x| \, dx =$

Let $f_n = \int_0^{\frac{\pi}{2}} \left(\sum_{k=1}^n \sin^{k-1} x\right) \left(\sum_{k=1}^n (2k-1) \sin^{k-1} x\right) \cos x \, dx$,where $n \in N$. Then $f_{21} - f_{20}$ is equal to $...........$.

If $[x]$ is the greatest integer not exceeding $x$,then $\int_{-0.5}^{1.5} x^2[x] d x=$