y = |x - 1| & y = 1
Required area = Area of region ABDA + Area of the region BDCB
\(= \int\limits ^1 _0y_1dx + \int\limits^2_1 y_2 dx\)
\(= \int\limits_0^1 - (x - 1) dx + \int\limits ^2_1(x - 1) dx\)
\(= - \left[\frac{x^2}{2}- x\right]^1_0 +\left [\frac{x^2}{2 }-x\right]^2_1\)
\(= -\left(\frac12 - 1\right)+ \left(\frac42 - 2 - \frac12 + 1\right)\)
\(= \frac12 + \frac12\)
= 1 square units
Hence, required bounded area = 1 square units.
