Is your 6570 a 2GB or 4GB version? If it's a 4GB version, then the only explanation I can come up with is Shared Memory is the sum of your Display Memory (1770) and your shared memory (2035) and it comes up slightly less than 4GB because of how conversion from bits to bytes, and is rounded up to "4 GB".
If it's a 2GB version, then the best I can explain it is, your "Display Memory" is the amount of video RAM allocated to driving your display. So you're being shown that you have 2035 MB of Graphics card memory, and 1770 MB of it is committed to rendering things on your display, the rest of the 235 MB is used for whatever other overhead your graphics card needs to process.
If Shared Memory is your RAM, then I'm assuming that means you have 4GB of regular RAM sticks installed on your motherboard.
In either case, I'm not sure why you would *want* an integrated graphics system if you have a dedicated graphics card, an integrated card won't be faster than your dedicated card. For that matter, why do you think you need more video RAM? Increased video RAM on a 6570 isn't going to improve performance much, you'd be better off just buying a new graphics card with more video RAM.