Assertion (A): The area of the region bounded by the line y -1=x, the x -axis and the ordinates x=-1 and x=1 is 2 square units. Reason (R): The area…

Assertion (A): The area of the region bounded by the line $\displaystyle \mathrm{y}-1=x$, the $\displaystyle x$-axis and the ordinates $\displaystyle x=-1$ and $\displaystyle x=1$ is $\displaystyle 2$ square units. Reason (R): The area of the region bounded by the curve $\displaystyle \mathrm{y}=\mathrm{f}(x)$, the $\displaystyle x$-axis and the ordinates $\displaystyle x=\mathrm{a}$ and $\displaystyle x=\mathrm{b}$ is given by $$\int_{\mathrm{a}}^{\mathrm{b}} \mathrm{f}(x) \mathrm{d} x . $$