\[ \large \int e^{x^2} \ e^x \ (2x^2+x+1) \, dx=e^{x^2} f(x)+C\]

Above shows an indefinite integral for some non-constant function \(f(x)\) and arbitrary constant \(C\).

If the minimum value of \(f (x)\) is equal to \(m\), then find the value of \(\left \lfloor -\dfrac{1}{m} \right \rfloor\).

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