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A strictly increasing and continuous function $f(x)$ intersects with its inverse $f^{-1}(x)$ at points $x=a$ and $x=b$, where $a$ and $b$ are integers.

If $\displaystyle \int_a^b[f(x) + f^{-1}(x)] \, dx = 17$, find $|a \times b|$.

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