$$P(x) = x^2 - 2x +5$$
Since a polynomial is defined and continuous everywhere, we only need to check the critical point and the boundaries.
$\dfrac{d}{dx}P(x) = 2x - 2$
Critical point: $2x-2 = 0\implies x = 1$ gives $P(x) = 4$, which is the minimum.
Boundaries: $\lim_{x \to \color{red}{0}^+} P(x) = \lim_{x \to \color{red}{2}^-} P(x) = 5$
Since $P(x)$ increases as $x$ goes farther away from the $1$, but $P(x)$ is defined on an open interval, $P(x)$ never attains a maximum!
Hence, e. None of the above is the correct answer.