The figure above shows the graph of \(f\). If \( f(x)=\int\limits_2^x g(t)   dt\), which of the following could be the graph of \(y=g(x)\) ?

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$$ f(x)=\int\limits_2^x g(t)   dt$$ $$ f'(x)=g(x) $$

The graph of the derivative shows a line with a positive slope.

\(g(x)\) must therefore be a horizontal line with a positive \(y\) value.

For example, a hypothetical answer: \(f'(x)=g(x)=1\)