I was thinking about the following problem:
If for $x \in R$, $\phi (x)$ denotes the integer closest to $x$ (If there are two such integers take the larger one),then $\int_{10}^{12}\phi (x)dx$ equals to
(a)$22$
(b)$11$
(c)$20$
(d)$12$.
I do not know how to proceed with the problem. Could someone point me in the right direction.Thanks in advance for your time.