Find the area of the region bounded by the curves y=1/x, y=x, y=x/4 where x>0 .
Have you drawn the graphs of each curve and hence shaded the required region? This is absolutely essential.
Then you should see that the area is given by
$\displaystyle A = \int_0^1 x - \frac{x}{4} \, dx + \int_1^2 \frac{1}{x} - \frac{x}{4} \, dx$.
The integral terminals come from considering the intersection points of $\displaystyle y = \frac{1}{x}$ with $\displaystyle y = x$ and $\displaystyle y = \frac{x}{4}$.