Trace \(g(x)\)

Calculus Level 3

\[ \large \displaystyle g(x)= \int_0^x f(t) \, dt \]

Let \(g\) and \(f\) be two real-valued functions satisfying the condition given above. The function \(f\) has a real root on \([-1,1]\) and is also strictly increasing on this interval.

What can be said about \(g\) in the given interval?

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