2010013804

Any positive real number $x$ can be written as $x=c+d$, where $c$ is an integer and $d\in [0,1)$. Then $c$ is called the integer part of $x$ and is denoted by $\left[x\right]$. Evaluate the following definite integral. $$\underset{3.1}{\overset{\frac{7}{2}}{\int }}\left[x\right]\mathrm{d}x$$