\[ \large \displaystyle\int_a^b \text{sgn(x) dx} = \ ? \]

**Details** :

- \(\text{sgn}(x) \) denotes the signum function of \(x\)

- \( \text{sgn}(x) = \begin{cases} 1 \quad,\quad x>0 \\ 0 \quad,\quad x=0 \\ -1 \quad,\quad x<0 \end{cases} \)

- \( a , b \in \Re\)

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