Answer
The conclusion (b) is correct.
Work Step by Step
Let $I = \mathop \smallint \limits_C^{} f\left( {x,y,z} \right){\rm{d}}s$.
Since $f\left( {x,y,z} \right) \ge m$ for some number $m$ and all points $\left( {x,y,z} \right)$ on $C$, we have
$I = \mathop \smallint \limits_C^{} f\left( {x,y,z} \right){\rm{d}}s \ge \mathop \smallint \limits_C^{} m{\rm{d}}s$
Since $m$ is constant, we get
$I \ge m\mathop \smallint \limits_C^{} {\rm{d}}s$
Let $L$ be the length of $C$. Thus, $I \ge mL$.
Therefore, the conclusion (b) is correct.
