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Area bounded by the line y=x, curve `y=f(x),(f(x)gtx,AA xgt1)` and the lines x=1,x=t is `(t-sqrt(1+t^2)-(1+sqrt2))` for all `tgt1`. Find `f(x)`.

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Area bounded by the line y=x, curve `y=f(x),(f(x)gtx,AA xgt1)` and the lines x=1,x=t is `(t-sqrt(1+t^2)-(1+sqrt2))` for all `tgt1`. Find `f(x)`.
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Correct Answer - `1+x+(x)/(sqrt(1+x^(2)))`
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