Find the area bounded by the curves $\displaystyle \mathrm{y}=|\mathrm{x}-1|$ and $\displaystyle \mathrm{y}=1$, using integration.

Area of the bounded region is$\displaystyle \int_0^1\left[1-(1-x)\right]dx+\int_1^2\left[1-(x-1)\right]dx$$\displaystyle \int_0^1 x\,dx+\int_1^2 (2-x)\,dx$$\displaystyle =\dfrac{x^2}{2}\Big]_0^1+\left[2x-\dfrac{x^2}{2}\right]_1^2$$\displaystyle =\dfrac{1}{2}+\left[4-\dfrac{4}{2}-2+\dfrac{1}{2}\right]$$\displaystyle =-1+2=1$