Trace g(x)g(x)

Calculus Level 3

g(x)=0xf(t)dt \large \displaystyle g(x)= \int_0^x f(t) \, dt

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

What can be said about gg in the given interval?

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