In a binned histogram, the probability density $f(x)$ is estimated as $\hat{f}(x) = \frac{n_i}{N \cdot w}$ where $n_i$ is the count in bin $i$, $N$ is total samples, and $w$ is bin width. If $N=500$, $w=2$, and we want to approximate $\int_0^4 f(x)\,dx$, given bin counts $n_1=50$ for $[0, 2)$ and $n_2=100$ for $[2, 4)$, what is the estimated integral value?