$$\int_0^{{\pi \over 2}} {\left| {\sin x - \cos x} \right|} \,dx$$ is equal to

$$\int_0^{{\pi \over 2}} {{e^{\sin x}}} \cos x\,xdx$$ is equal to

What is $\int _{n}^{n+1}(x-[x])dx$, where [.] is the greatest integer function and n is natural number?

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?