Let $$f:[0, \infty)$$ \rightarrow R be a continuous function such that $$f(x)=1-2x+ \int_{0}^{x} e^{x-t} f(t) dt$$ for all $$x \in [0,\infty]$$ Then, which of the following statement(s) is (are) TRUE?

A

The curve 𝑦 = 𝑓(𝑥) passes through the point (1, 2)

B

The curve 𝑦 = 𝑓(𝑥) passes through the point (2, −1)

C

The area of the region $${(x,y) \in [0,1] \times R:f(x) \leq y \leq \sqrt{1-x^{2}}} is \frac{\pi-2}{4}$$

D

The area of the region $${(x,y) \in [0,1] \times R:f(x) \leq y \leq \sqrt{1-x^{2}}} is \frac{\pi-1}{4}$$