$5 \cdot 14$ If the function $y=\frac{1}{2}\left(x^{2}-100 x+196+\left|x^{2}-100 x+196\right|\right)$, then when the independent variable $x$ takes the 100 natural numbers $1,2,3, \cdots, 100$, the sum of the function values is
(A) 540.
(B) 390.
(C) 194.
(D) 97.
(China Junior High School Mathematics League, 1999)
[Solution] $\because x^{2}-100 x+196=(x-2)(x-98)$,
$\therefore$ when $2 \leqslant x \leqslant 98$,
$$
\left|x^{2}-100 x+196\right|=-\left(x^{2}-100 x+196\right) \text {. }
$$

Therefore, when the independent variable $x$ takes $2,3, \cdots, 98$, the function value is 0.
And when $x$ takes $1,99,100$,
$$
\left|x^{2}-100 x+196\right|=x^{2}-100 x+196 .
$$

Thus, the required sum is
$$
\begin{aligned}
& (1-2)(1-98)+(99-2)(99-98)+(100-2) \cdot(100-98) \\
= & 97+97+196=390 .
\end{aligned}
$$

Therefore, the answer is $(B)$.