Let \(f:[0,\infty )\to \mathrm{ℝ}\)be differentiable function such that \(\mathrm{f}(\mathrm{x})=1-2\mathrm{x}+{\int }_{…

Let \(f:[0,\infty )\to \mathrm{ℝ}\)be differentiable function such that \(\mathrm{f}(\mathrm{x})=1-2\mathrm{x}+{\int }_{0}^{\mathrm{x}}{\mathrm{e}}^{\mathrm{x}-\mathrm{t}}\mathrm{f}(\mathrm{t})\mathrm{dt}\) for all \(\mathrm{x}\in [0,\infty )\).
Then the area of the region bounded by \(\mathrm{y}=f(\mathrm{x})\) and the coordinate axes is

[JEE Main 2025, 4 Apr (Shift 1)]