Let f:[-2,3] →[0, ∞) be a continuous function such that f(1-x)=f(x) for all x ∈[-2,3]. If R_1 is the numerical value of the area of the region…

Let $\displaystyle f:[-2,3] \rightarrow[0, \infty)$ be a continuous function such that $\displaystyle f(1-x)=f(x)$ for all $\displaystyle x \in[-2,3]$. If $\displaystyle \mathrm{R}_1$ is the numerical value of the area of the region bounded by $\displaystyle y=f(x), x=-2$, $\displaystyle x=3$ and the axis of $\displaystyle x$ and $$\mathrm{R}_2=\int_{-2}^3 x f(x) \mathrm{d} x \text {, then : } $$