Answer
$6$
Work Step by Step
Our aim is to integrate the integral as follows:
$\int^1_{-1} \int^1_0 \int^2_0 (x+y+z) \space dy \space dx \space dz=\int^1_{-1} \int^1_0 =[xy+\dfrac{y^2}{2}+zy]^2_0 \space dx \space dz \\=\int^1_{-1} \int^1_0 (2x+2+2z) dx dz \\= \int^1_{-1}[x^2+2x+2(z)(x)]^1_0 dz\\ = \int^1_{-1}(3+2z)$ dz
or, $=[3z+z^2]^1_{-1}$
or, $=6$
