# Don't definite Integrals find area?

1. Dec 16, 2007

### lLovePhysics

I'm confused here.. My definite integral doesn't match by Riemman Sum... and it should right? I think that I have not integrated correctly. Can someone help me spot the problem? Thanks.

Find the Area of the region bounded by:
$$f(x)=5-x^2$$ , [-2, 1]

Using the Riemma Sum idea (limit of the sum of rectangles as the number of rectangles approaches infinity), I got 12 units^2 as my area, which is correct.

However, using definite integrals and the Fundamental Theorem of Calculus, I get:

$$\int_{-2}^{1} (5-x^2)dx}$$

$$=-\frac{x^3}{3}\biggl] ^{1}_{-2}$$

Which equals -3 ???

2. Dec 16, 2007

### rocomath

5x - 1\3 * x^3

3. Dec 16, 2007

### lLovePhysics

Noooo.. I can't believe I made another stupid mistake!! Thanks Roco