If $$\mathrm{f}(x)=\left\{\begin{array}{ll}\mathrm{e}^{\cos x} \sin x & , \text { for }|x| \leq 2 \\ 2, & \text { otherwise }\end{array}\right.$$, then $$\int_\limits{-2}^3 \mathrm{f}(x) \mathrm{d} x$$ is equal to

The value of $$\int_\limits0^\pi\left|\sin x-\frac{2 x}{\pi}\right| \mathrm{d} x$$ is

$$\int_\limits0^4|2 x-5| d x=$$

Let $$f:[-1,2] \rightarrow[0, \infty)$$ be a continuous function such that $$\mathrm{f}(x)=\mathrm{f}(1-x), \forall x \in[-1,2]$$

Let $$\mathrm{R}_1=\int_{-1}^2 x \mathrm{f}(x) \mathrm{d} x$$ and $$\mathrm{R}_2$$ be the area of the region bounded by $$y=\mathrm{f}(x), x=-1, x=2$$ and the $$\mathrm{X}$$-axis, then $$\mathrm{R}_2$$ is