Let [t] denote the largest integer less than or equal to t. If ∫_0^3([x^2]+[x^2/2]) d x=a+b √ 2 -√ 3 -√ 5 +c √ 6 -√ 7, where a, b, c ∈ Z, then a+b+c…

Let $\displaystyle [t]$ denote the largest integer less than or equal to $\displaystyle t$. If $\displaystyle \int_0^3\left(\left[x^2\right]+\left[\frac{x^2}{2}\right]\right) d x=a+b \sqrt{2}-\sqrt{3}-\sqrt{5}+c \sqrt{6}-\sqrt{7}$, where $\displaystyle a, b, c \in Z$, then $\displaystyle a+b+c$ is equal to $\displaystyle \_\_\_\_$.