Let the curve $y=y(x)$ be the solution of the differential equation, $\frac{d y}{d x}=2(x+1)$. If the numerical value of area bounded by the curve $y=y(x)$ and $x$-axis is $\frac{4 \sqrt{8}}{3}$, then the value of $y(1)$ is equal to $\_\_\_\_$ .
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