I have tried to get aother integral representation for the Golden ratio i have got the following representation . This integral is defined as : $$I(t)=\int\limits_{0}^{t}(\exp{(\sqrt{x}-x^2)} )^ \text{erf(x)}\ \text{d}x,$$ and this gives $1.618...$ for $t \to +\infty$ with approximation of $10^{-3}$ as shown here in wolfram alpha and it's seems that is closed nicely to Golden ratio for $t \in [2,3]$ for instance we have $t=2.75..$ and also for $t=e$ , Now my question here is :
Question: Is it possible to say that :For $t\geq 2$ ,$\int\limits_{0}^{t}(\exp{(\sqrt{x}-x^2)} )^ \text{erf(x)}\ \text{d}x$ could be another integral representation of Golden ratio ?