Let $f:\left[0,\infty \right)\to R$be a continuous function such that $f\left(x\right)=1-2x+{\int }_0^x{e}^{x-t}f\left(t\right)dt$for all $x\in \left[0,\infty \right)$. Then, which of the following statement(s) is (are) TRUE?The curve $y=f\left(x\right)$passes through the point $\left(1,2\right)$(b) The curve $y=f\left(x\right)$passes through the point $\left(2,-1\right)$(c) The area of the region $\left\{\left(x,y\right)\in \left[0,1\right]\times R:f\left(x\right)\le y\le \sqrt{1-x^2}\right\}$is $\frac{\pi -2}{4}$(d) The area of the region $\left\{\left(x,y\right)\in \left[0,1\right]\times R:f\left(x\right)\le y\le \sqrt{1-x^2}\right\}$is $\frac{\pi -1}{4}$

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