$\int(\int\phi(a-z)dz)dz=\Phi(a-z)$

Question

Lets assume $\phi(a-z)$ is integrable.

Can I conclude that the following integral

$$\int\left(\int\phi(a-z)dz\right)dz$$

Can be expressed by a function $$\Phi(a-z).$$

So in result: $$\int\left(\int\phi(a-z)dz\right)dz=\Phi(a-z)$$

Answer 1

$\int\left(\int\phi(a-z)~dz\right)dz$

$=z\int\phi(a-z)~dz-\int z~d\left(\int\phi(a-z)~dz\right)$

$=z\int\phi(a-z)~dz+\int z~\phi(a-z)~dz$