Riemann integral is f integrable on I?

Question

P={$0,(2-\frac{1}{n}), (2+\frac{1}{n}), 4$} and interval I=[0,4] Is f integrable on I?

I have found that $U(f,P)$=$8+\frac{2}{n}$ and $L(f,P)$=$8-\frac{2}{n}$ So does this mean that we get bounds for infimum and supremum and f is integrable?

Answer 1

I did not check whether the values that you got are correct or not but, yes, if they are correct, then it follows from them that:

1. $f$ is Riemann-integrable;
2. $\displaystyle\int_0^4f(x)\,\mathrm dx=8$.