For $$\left| {x + 1} \right|$$ critical point, x + 1 = 0 $$\Rightarrow$$ x = $$-$$1

For $$\left| {x + 2} \right|$$ critical point, x + 2 = 0 $$\Rightarrow$$ x = $$-$$2

For $$\left| {x + 3} \right|$$ critical point, x + 3 = 0 $$\Rightarrow$$ x = $$-$$3

For $$\left| {x + 4} \right|$$ critical point, x + 4 = 0 $$\Rightarrow$$ x = $$-$$4

For $$\left| {x + 5} \right|$$ critical point, x + 5 = 0 $$\Rightarrow$$ x = $$-$$5

Here maximum function is represent by the dotted line.

$$\therefore$$ Point of intersection A of line y = $$-$$x $$-$$1 and y = x + 5 :

$$ - x - 1 = x + 5$$

$$ \Rightarrow 2x = - 6$$

$$ \Rightarrow x = - 3$$

$$\therefore$$ $$y = - 3 + 5 = 2$$

$$\therefore$$ Point $$A = ( - 3,2)$$

$$\therefore$$ $$\int_{ - 6}^0 {f(x)dx} $$

$$ = \int_{ - 6}^{ - 3} {( - x - 1)dx + \int_{ - 3}^0 {(x + 5)dx} } $$

$$ = \left( { - {{{x^2}} \over 2} - x} \right)_{ - 6}^{ - 3} + \left[ {{{{x^2}} \over 2} + 5x} \right]_{ - 3}^0$$

$$ = \left[ {\left( { - {9 \over 2} + 3} \right) - \left( { - {{36} \over 2} + 6} \right)} \right] + \left[ {0 - \left( {{9 \over 2} - 15} \right)} \right]$$

$$ = \left( { - {3 \over 2} + 12} \right) + {{21} \over 2}$$

$$ = + {{21} \over 2} + {{21} \over 2}$$

$$ = 21$$