I am asked to determine the underestimation of an indicator function on the interval [0,2], defined as follows: $\int_{0}^{2} \mathbf{1}_{1}\,dx$.
Intuitively, I'd say the answer is 0, since we have one point on the interval and the integral of a point is always zero, however is there a way to work this out more formally?
Edit: and how would the formal way of the overestimation go exactly?