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 A_{1} = $\frac{1}{2}*7*7 = \frac{49}{2}$
For smaller triangle, base = 1, height = 1 $\therefore$ Area A_{2} = $\frac{1}{2}*1*1 = \frac{1}{2}$
Total required area = A_{1 }+ A_{2} = $\frac{49}{2} + \frac{1}{2} = 25$