Mathematics - Application of Derivative Question with Solution | TestHub

Let $\mathrm{g}(\mathrm{x})={\int }_{1-\mathrm{x}}^{1+\mathrm{x}}\mathrm{t}\left|{\mathrm{f}}^{\prime }(\mathrm{t})\right|\mathrm{dt}$, where $\mathrm{f}(\mathrm{x})$ does not behave like a constant function in any interval (a, b) and the graph of $y=f^{\prime }(x)$ is symmetric about the line $x=1$. Then