## 7.1. Riemann Integral

### Examples 7.1.13(b):

According to part 2 of the previous result we know thatforf(x) dx = f(x) dx + f(x) dx

*a < c < b*. Let

*a = -1*,

*c = 1*, and

*b = 2*. Then we have:

andf(x) dx = x^{2}dx = 1/3 (1^{3}- (-1)^{3}) = 2/3

Thereforef(x) dx = 3 dx = 3 (2 - 1) = 3

Here we computedf(x) dx = 2/3 + 3 = 11/3

*x*similarly than in a previous example.

^{2}dx