The following is the graph of a continuous function $y = f ( x )$. When the inverse function $g ( x )$ of function $f ( x )$ exists and is continuous on the interval $[ 0,1 ]$, the limit value $$\lim _ { n \rightarrow \infty } \sum _ { k = 1 } ^ { n } \left\{ g \left( \frac { k } { n } \right) - g \left( \frac { k - 1 } { n } \right) \right\} \frac { k } { n }$$ has the same value as which of the following? [4 points] (1) $\int _ { 0 } ^ { 1 } g ( x ) d x$ (2) $\int _ { 0 } ^ { 1 } x g ( x ) d x$ (3) $\int _ { 0 } ^ { 1 } f ( x ) d x$ (4) $\int _ { 0 } ^ { 1 } x f ( x ) d x$ (5) $\int _ { 0 } ^ { 1 } \{ f ( x ) - g ( x ) \} d x$
The following is the graph of a continuous function $y = f ( x )$.
When the inverse function $g ( x )$ of function $f ( x )$ exists and is continuous on the interval $[ 0,1 ]$, the limit value
$$\lim _ { n \rightarrow \infty } \sum _ { k = 1 } ^ { n } \left\{ g \left( \frac { k } { n } \right) - g \left( \frac { k - 1 } { n } \right) \right\} \frac { k } { n }$$
has the same value as which of the following? [4 points]\\
(1) $\int _ { 0 } ^ { 1 } g ( x ) d x$\\
(2) $\int _ { 0 } ^ { 1 } x g ( x ) d x$\\
(3) $\int _ { 0 } ^ { 1 } f ( x ) d x$\\
(4) $\int _ { 0 } ^ { 1 } x f ( x ) d x$\\
(5) $\int _ { 0 } ^ { 1 } \{ f ( x ) - g ( x ) \} d x$