The limits of integration are typically given in the integral itself. If not, they can be determined by looking at the graph of the function being integrated and finding the points where the graph intersects the x-axis.
The first step is to rewrite the integral in a simpler form by using algebraic techniques such as factoring, substitution, or trigonometric identities.
The appropriate integration technique is chosen based on the form of the integral. Some common techniques include substitution, integration by parts, and partial fractions.
Some common mistakes to avoid include forgetting to change the limits of integration when using substitution, forgetting to distribute the derivative when using integration by parts, and making errors in algebraic simplification.
You can check the accuracy of your solution by taking the derivative of the antiderivative you calculated and comparing it to the original function. If they are equal, then your solution is correct.