There is an easier way to do the problem. You can use what's called integration but that is a calculus topic.
One way you can solve it is by graphing.
You can draw the graph of the function (which is linear) and find the area under the curve. When you calculate the area under the curve (which is a triangle) you only take into account the area from 0 to 30. Also, if any piece of the graph from 0 to 30 is below the x axis then you have to subtract that portion from the area that is above the x axis.
If you have a graphing calculator I can show you an even simpler way.
Oh wait...I have to apologize for being retarded. You can't solve this with integration because it's a summation (it's been awhile). Unfortunately, you have to add all those #'s together because a summation is not the exact answer but an estimation. An integral, on the other hand, is the exact answer.