Let a function `f(x)` be defined in `[-2, 2]` as
`f(x) = {{:({x}",",, -2 le xlt -1), (|"sgn "x|",",,-1le x le 1),({-x}",",, 1 lt xle 2):}` where `{x}` and sgn `x` denote fractional part and signum functions, respectively. Then find the area bounded by the graph of `f(x)` an the x-axis.

Explanation

To find the area bounded by the graph of the function \( f(x) \) and the x-axis over the interval \([-2, 2]\), we will break down the function into its respective segments and calculate the area for each segment.

### Step 1: Define the function segments
The function \( f(x) \) is defined as follows:
- For \( -2 \leq x < -1 \): \( f(x) = \{x\} \) (the fractional part of \( x \))
- For \( -1 \leq x \leq 1 \): \( f(x) = \text{sgn}(|x|) \) (the signum function)
- For \( 1 < x \leq 2 \): \( f(x) = \{-x\} \) (the fractional part of \( -x \))

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