The area of the region bounded by the curves $y=|x-2|,$ $x=1,x=3$ and the $x$ -axis is

The region is bounded by the V-shaped graph of $y=|x-2|,$ vertical lines $x=1,x=3,$ and the $x$ -axis.
The vertex of the V is at $(2,0).$
The area can be calculated as the sum of two integrals or two triangles:From $x=1$ to $x=2:y=2-x.$ Area $={\int }_1^2(2-x)dx=[2x-\frac{x^2}{2}{]}_1^2=(4-2)-(2-1/2)=2-1.5=0.5$.From $x=2$ to $x=3:y=x-2.$ Area $={\int }_2^3(x-2)dx=[\frac{x^2}{2}-2x{]}_2^3=(4.5-6)-(2-4)=-1.5+2=0.5$.Total Area $=0.5+0.5=1$.
Alternatively, the area consists of two identical right-angled triangles with base $1$ (from $1$ to $2$ and $2$ to $3$) and height $1$ (at $x=1,y=1$ and at $x=3,y=1$).
Total Area $=2\times (\frac{1}{2}\times 1\times 1)=1.$