Let $f:[-2, 3] \to [0, \infty)$ be a continuous function such that $f(1-x) = f(x)$ for all $x \in [-2, 3]$. If $R_1$ is the numerical value of the area of the region bounded by $y = f(x)$,$x = -2$,$x = 3$ and the $x$-axis,and $R_2 = \int_{-2}^3 x f(x) dx$,then:

  • A
    $3R_1 = 2R_2$
  • B
    $2R_1 = 3R_2$
  • C
    $R_1 = R_2$
  • D
    $R_1 = 2R_2$

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