x to the end + 1

Something unusual is happening in the definition of the relationships in mathematics. There seems to be a disconnect between either my understanding of the math or its relationship as a description of the universe. The idea that the Σ of a trigonometric is defined as trigonometric value is reasonable as it is a continuously varying sum of the same type. It does have a different aspect when used in the summation of integral calculus. I can perform the calculations as well as anyone with a memory to associate the anecdotal methods to application , but something more interesting is happening in the foundation of the process.