What is a (Riemann) integral?

Let f be a function on [a,b] and be a partition P of [a,b]. Let where is the minimum (actually greatest lower bound) of f on . Similarly, where is the maximum of f on .

The integral is that unique number with for every partition P.

That's really the definition of integral. The great fundamental theorem of calculus allows "easy" computation of G.

In particular a partition with n=1, has and and so

So for your specific problem