you want to minimize the area, so this is an optimization problem. those are all done the same way, so you should have an idea of how to proceed.
the area will be given by an integral, first set this up. find the limits and then set up the integral for (top function) - (bottom function) over those limits. you want to minimize the resulting intral. note that you may not have to do the integral, though it is simple enough to do if you choose. you can apply the second fundamental theorem of calculus to find the derivative of the function defined as the integral
substitution works here. first note that you can write the integral as $\displaystyle \int_0^1 \frac {x^2 - x}{x \ln x}~dx$ by multiplying by $\displaystyle \frac xx$. Now, let $\displaystyle u = \ln x$ and continue via integration by substitution.
Welcome!
...you meant to say "help" as opposed to "thanks" right?