Integrating Over Absolute Values

Calculus Level 3

f(x)={1x,x1x1,x>1 f(x) = \begin{cases}{1-|x|}, && {|x|\>\le\>1} \\ {|x|-1,} && {|x|>1}\end{cases}

g(x)=f(x1)+f(x+1)g(x) = f(x-1)+f(x+1).

Given the two functions above, what is the value of 35g(x)dx \displaystyle \int _{ -3 }^{ 5 }{ g(x) \mathrm{d}x } ?

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