First find the curve then area

Calculus Level pending

Let \( f\left( x \right)\) be a differentiable function such that

\( f\left( x+y \right) ={ e }^{ x }f\left( y \right) +{ e }^{ y }f\left( x \right) \)

for all \( x,y \)

And Given that \( f^{ ' }\left( x \right) =1 \)

Find the Area bounded by the curve and x axis


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