# 2015_32 Simple and elegant Part 3

**Calculus**Level pending

Let \(f\left( x \right) \) be a real valued function not identically zero such that \[f\left( x+{ y }^{ n } \right) =f\left( x \right) +{ (f(y)) }^{ n }\quad \forall x,y\epsilon R\] where \(n\epsilon N(n\neq 1)\) and \(f^{ ' }\left( 0 \right) \ge 0\) we may get an explixity form of the function \(f\left( x \right) \).

Then the value of \(\int _{ 0 }^{ 1 }{ f\left( x \right) dx } \) is?

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