Calculating the area under the graph of a function.

I know this question might be very trivial for many of you, but I would appreciate if you take a look, in the following question I'm asked to calculate the area that is under the function's graph in interval $[0,3]$. I tried to use the idea of cutting the shape into rectangles and triangles and try to evaluate in what range the area could be, and this is what they are asking for.

here is the graph:

and here is what I did:

I said that the area is surely bigger than the area I selected in picture A, which turns out to be 12. and did same principal to find the maximum area but calculating rectangles and in some cases removing areas of triangles to be more accurate, and what I got is 15.

so my final answer is that $12<area<15$ and for some reason its wrong.

can someone tell me why?

• What is $\color{red} {10}$? – zoli Mar 20 '15 at 11:45
• My eyesight is not good enough. But I can see $1$ for the height of the red area. – zoli Mar 20 '15 at 11:50
• @zoli sorry, my mistake, corrected. – Firas Ali Abdel Ghani Mar 20 '15 at 11:57
• @zoli its not 10, it just indicates the height, which is 1.0 – Firas Ali Abdel Ghani Mar 20 '15 at 11:58
• Although the top of graph B is cut off, it looks like the area should be 16, not 15. – Mattos Mar 20 '15 at 12:20