@Carl Love 

I understand the substitution of y and z, and thereby the integrand, however I do not understand the differential. 

I have calculated the differential to be

(rho*cos(theta)*sin(phi))^2 + (rho*sin(theta)*sin(phi))^2 + (rho*cos(phi))^2 =

rho^2 * (sin^2(theta)*sin^2(phi)+cos^2(theta)+sin^2(phi)+cos^2(phi) = rho^2

And why is it you multiply the intregral and the differential?

@H-R Thanks for the response!

The function I want to integrate is f(x,y,z)=y

And I want to do it in regards to the domain (0 <= y, x^2+y^2+z^2 <= 1)

Any suggestions how to fix my input?