By using the properties of definite integrals, the value of \(\int_{-5}^{5}\left(x+2\right)dx\) is

\(20\)

The correct answer is Option (3) → \(20\)

\(I=\int\limits_{-5}^{5}\left(x+2\right)dx\)

$=\int\limits_{-5}^{0}(x+2)dx+\int\limits_{0}^{5}(x+2)dx$

$=\left[\frac{x^2}{2}+2x\right]_{-5}^{0}+\left[\frac{x^2}{2}+2x\right]_{0}^{5}$

$=\left[0-\frac{25}{2}+10\right]+\left[\frac{25}{2}+10\right]$

$=20$