The value of the integral I=∫^2_-1|x|dx is :

The correct answer is Option (3) → $\frac{5}{2}$

$I=\int\limits^{2}_{-1}|x|dx=\int\limits_{-1}^0-xdx+\int\limits^{2}_0xdx$

$=\left[\frac{-x^2}{2}\right]_{-1}^0+\left[\frac{x^2}{2}\right]^{2}_0$

$=\frac{4}{2}+\frac{1}{2}=\frac{5}{2}$