Building a Double Integral Calculator

Hey there guys,

I saw a lot of materials on calculating Double Integrals here on the site, but none of them made everything I wanted clearly, so I decided to make my own. In that sense, I want to see three things when I'm calculating a Double Integral:

(i) Step-by-step algebraic process, until the final numeric result: Most of the time I make 1 or 2 little mistakes when calculating Double Integrals, but those lead to very different results, so I want to check every step of my calculus.

(ii) Domain Sketching: Sometimes I don't even know how the domain is going to look like, so I end up putting wrong boundaries on the integral. I'm pretty sure GeoGebra can sketch any domain better than I do haha.

(iii) 3D Representation: Even when I do get right results, most of the time I don't know VISUALLY what I'm calculating. The goal here is to show the volume of the "thing" which I'm calculating.

I came across some problems though, and I've tried looking for solutions here on the forum, but since I'm not a advanced user, I didn't find any. Here are them:

1) The integral constants keep showing up: I want this calculator ready to be used right when someone open it up, but every time I do open it, the algebraic result is filled with integral constants. I wouldn't consider those when I'm calculating a volume.

2) I don't know how to code (iii): What I want is that the functions I type in on the algebraic calculator ( f(x) & g(x) ) show up as shapes in the "Volume Representation" screen, so they can be limited inferiorly by the x-y plane and superiorly by f(x,y), forming a "thing" which the Double Integral is calculating the volume.

I'll post the .ggb file and some screenshots of the calculator here so you guys can understand what I'm asking.

Thanks in advance!