Exponential Integration

Calculus Level 4

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

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 $\left \lfloor -\dfrac{1}{m} \right \rfloor$ .

4 5 -3 0 -2 2 1