Graphical method is easier. Graph of $\left | 3-x \right |$ is as follows :
We just need to find area of the shaded portion, it is nothing but area of two triangles.
For larger triangle, base = 7, height = 7 $\therefore$ Area A1 = $\frac{1}{2}*7*7 = \frac{49}{2}$
For smaller triangle, base = 1, height = 1 $\therefore$ Area A2 = $\frac{1}{2}*1*1 = \frac{1}{2}$
Total required area = A1 + A2 = $\frac{49}{2} + \frac{1}{2} = 25$