If you are learning about integration, there are some excellent online resources to help you. You can of course check your work with WolframAlpha and note that if you ask for a definite integral WolframAlpha will also return a visual representation of the integral, illustrating the area found. This is particularly helpful where parts of the curve are above the x axis and parts below. (You can see further calculus examples as part of Slideshow 4 on the WolframAlpha page).
If you use the Numerical integration utility and grapher from zweigmedia’s Finite mathematics and Applied Calculus you can choose your own function, then compare the actual value of the integral with that found by various approximate methods.