$\mathrm { f } ( x )$ is a function for which $$\int _ { 0 } ^ { 3 } ( \mathrm { f } ( x ) ) ^ { 2 } \mathrm {~d} x + \int _ { 0 } ^ { 3 } \mathrm { f } ( x ) \mathrm { d } x = \int _ { 0 } ^ { 1 } \mathrm { f } ( x ) \mathrm { d } x$$ Which of the following claims about $\mathrm { f } ( x )$ is/are necessarily true? I $\mathrm { f } ( x ) \leq 0$ for some $x$ with $1 \leq x \leq 3$ II $\int _ { 0 } ^ { 3 } \mathrm { f } ( x ) \mathrm { d } x \leq \int _ { 0 } ^ { 1 } \mathrm { f } ( x ) \mathrm { d } x$ A neither of them B I only C II only D I and II
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$\mathrm { f } ( x )$ is a function for which
$$\int _ { 0 } ^ { 3 } ( \mathrm { f } ( x ) ) ^ { 2 } \mathrm {~d} x + \int _ { 0 } ^ { 3 } \mathrm { f } ( x ) \mathrm { d } x = \int _ { 0 } ^ { 1 } \mathrm { f } ( x ) \mathrm { d } x$$
Which of the following claims about $\mathrm { f } ( x )$ is/are necessarily true?\\
I $\mathrm { f } ( x ) \leq 0$ for some $x$ with $1 \leq x \leq 3$\\
II $\int _ { 0 } ^ { 3 } \mathrm { f } ( x ) \mathrm { d } x \leq \int _ { 0 } ^ { 1 } \mathrm { f } ( x ) \mathrm { d } x$
A neither of them\\
B I only\\
C II only\\
D I and II