Definite integration

Definite integration follows the same normal steps as indefinite integration.

Steps

We first integrate the expression (but don’t add the +c term).
Then we substitute the upper limit into the integrated expression - the upper limit is at the top of the integral sign - the a in \int_a^b.
We next substitute the lower limit into the integrated expression - the lower limit is at the bottom of the integral sign - the b in \int_a^b.
Finally, we subtract the result of step 3 from the result of step 2 to get the final answer. We always take away the integral found from the lower limit from the upper limit.

If we have the unintegrated function we write it like this:

\int_b^a f(x) \, dx

If we let g(x) be the intergral of f(x), then we can write:

\left[g(x)\right]_b^a

Question	Answer
What are the four steps for definite integration?	1. Integrate the expression without adding +c. 2. Substitute the upper limit (a in \int_a^b) into the integrated expression. 3. Substitute the lower limit (b in \int_a^b) into the integrated expression. 4. Subtract the result of step 3 from the result of step 2.
When evaluating \int_b^a f(x) \, dx, how do you combine the results from substituting the limits?	We subtract the value obtained from the lower limit (b) from the value obtained from the upper limit (a).
If g(x) is the integral of f(x), what notation is used for definite integration?	\left[g(x)\right]_b^a is used.