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?