Final answer:
Most of the energy from ATP comes from breaking its high-energy phosphoanhydride covalent bonds during hydrolysis, releasing energy for cellular activities.
Step-by-step explanation:
The energy that is released when breaking the bonds in ATP primarily comes from the breaking of covalent bonds, particularly the phosphoanhydride bonds. These are the bonds that link the phosphates in the ATP molecule. When ATP is hydrolyzed into ADP (adenosine diphosphate) and an inorganic phosphate group (Pi), the breakage of these high-energy bonds releases a considerable amount of energy that can be utilized in various cellular reactions and processes.