My question is about a). I see that:

$\displaystyle \int^e_1\frac{\sqrt(ln(x))}{x}\;dx=\int^1_0\sqrt(u )\;du$

those are equivalent because I graphed both of them. In the screenshots the area is listed in the lower left hand corner. Algebraically I am having a tougher time figuring out how those are equal. What keeps getting to me is how was it determined that the interval changes from 1 to e (to) 0 to 1.

Thanks in advance for any responses...