19.6.1.8 Lebesgue measure and integration

Condition: Find the Lebesgue integral \[ \begin{array}{l} \int_{[0 ; \infty)} f d \mu \text { from the function } f(x)=\frac{1}{n^{2}(n+1)}, \\ \text { if } x \in[(n-1) n ; n(n+1)), n \in \mathbb{N} . \end{array}\]