I'm not entirely 100% on what "integrated" means. But if it means that the card is stuck to the motherboard and is not exchangeable, then it is integrated. I fiddled with it to make sure (no facepalms please ) and I also later found a forum post on the internet saying so (no I do not go about things the wrong way).
Technically, yes, the CPU and GPU are stuck to the motherboard, but the term would be "soldered". Those parts are soldered to the motherboard. There's theoretically ways to remove those parts and replace them with something else, but you'd need special tools and a lot of skill to pull off such a feat.
If my understanding is correct, an "integrated" GPU means that the GPU is literally part of the silicon of the CPU*. The GPU is integrated into the CPU. Since space is limited in the CPU, it has to get its memory somewhere else. This usually takes the form of sharing the system memory. It gets memory allocated to it, and this is called "shared memory"
A dedicated GPU, on the other hand, is an independent piece of silicon, dedicated entirely to being a GPU. In almost all cases, it gets its own independent pool of memory to work with. This is "dedicated memory". This memory is usually substantially faster than the system memory.
*I'm completely ignoring motherboard integrated graphics, since that's a whole 'nother can of worms, and that hasn't been a thing since the Core 2 era, around 2010.
The laptop comes with two graphics cards, one intel with 1 GB whatever, and the Nvidia card that I think is the trouble with iirc 2 GB whatever. I believe those whatever numbers are the dedicated memory, right?
See, Windows (I'm assuming Windows, tell me if it's something else) is being somewhat disingenuous when it tells you that the Intel one has 1 GB. What happened here is that the system (specifically the BIOS) tells the Intel GPU that it can have 1 GB of system memory to work with. This isn't dedicated memory, this is shared memory.
The Nvidia card sounds about right. (Technically speaking, even dedicated GPUs have shared memory. This is more for use in "emergency" situations, where there isn't enough dedicated memory to fit stuff (textures, shaders) into. The downside of this is that shared memory is
really slow compared to dedicated memory. If you've ever turned up the Textures setting on a game up too far, and the game lags like hell, it's probably run out of dedicated memory, and it's loading textures into shared memory.)