Let f:[0, ∞) → R be a differentiable function such that f(x)=1-2 x+∫_0^x e^x-t f(t) d t for all x ∈[0, ∞). Then the area of the region bounded by…

Let $\displaystyle f:[0, \infty) \rightarrow \mathbb{R}$ be a differentiable function such that $\displaystyle f(x)=1-2 x+\int_0^x e^{x-t} f(t) d t$ for all $\displaystyle x \in[0, \infty)$. Then the area of the region bounded by $\displaystyle y=f(x)$ and the coordinate axes is