$\int_{-2}^{1} [x+1] \, dx =$ (Where $[x]$ is the greatest integer function not greater than $x$)

Let $y = \{x\}^{[x]}$ where $\{x\}$ denotes the fractional part of $x$ and $[x]$ denotes the greatest integer $\le x$. Then $\int_{0}^{3} y \, dx = $

The value$(s)$ of $\int_0^1 \frac{x^4(1-x)^4}{1+x^2} d x$ is (are)

The value of $\int_0^2 [x^2] dx$ is (where $[x]$ denotes the greatest integer function not greater than $x$)

If $f(y) = e^y$,$g(y) = y$ for $y > 0$,and $F(t) = \int_{0}^{t} f(t - y) g(y) dy$,then:

If the integral $525 \int_0^{\frac{\pi}{2}} \sin 2 x \cos^{\frac{11}{2}} x \left(1+\cos^{\frac{5}{2}} x\right)^{\frac{1}{2}} d x$ is equal to $(n \sqrt{2}-64)$,then $n$ is equal to