Limits + Area Problem

[blackrosedog]

Hi! I've been having some trouble with this problem on a practice test in my Precalculus class (I decided to post this in Calculus because we're doing introductory Calc lessons; hope that's okay!). I did it the same way the people at Calc-chat.com did a similar problem from my book, but I keep getting 20. The answer should be 140, says my key!
Here's the question:
"Use the limit process to find the area of the region between f (x)=4x+6 and the x-axis on the interval [0,3]"
Here's a picture of my work (sorry about the messiness... I hope it's readable!!):
http://img31.imageshack.us/img31/8300/photo05241808.jpg
I'm really struggling with this topic and I just did it step-for-step like the Calc-chat problem, which usually works, but not this time apparently... What did I do wrong??
Thanks for your time!

 

[tkhunny]

You can always try a manual limit process to try to get the hang of it.

One left interval: 3*0 = 0 -- Well, that's not very helpful. It's a lower bound.

Three left intervals: 1*0 + 1*10 + 1*14 = 24
Three right intervals: 1*10 + 1*14 + 1*18 = 42

Okay, it's bracketed, now.