It is most likely the graphics. Intel HD Graphics are really made for basic computing usage. That is, they don't have very good support for OpenGL and DirectX (Graphics API's). I can get 60 FPS or so with a Pentium P6200 and Intel HD Graphics though, so perhaps you could install Optifine or lower your settings?
Also, you didn't exactly specify what you meant by 'slow' so it's a bit hard to diagnose your problem.