# Math Help - Proper Integration

1. ## Proper Integration

Hello I am new.

Question:
Find the area bounded by the graph of each of the following functions, the x-axis and the given co-ordinates. Sketch the graph in case.
f(x)=2-x-x^2 ; x=0 to x=2.

My attempt:
=2x-(x^2/2)-(x^3/3)
=(0) - (2(2) - (2)^2/2) - (2)^3/3)
=0- (4-2-(8/3))
=0 - (-2/3)
Absolute value gives me:
2/3
But the answer is not right it is:
3.
3. The graph of $y= 2- x- x^2$ crosses the x-axis at x= 1. The region bounded by those graphs has a portion above the x-axis and a portion below it. Since area is always positive and integrating a negative function give a negative result the area is
$\int_0^1 (2- x- x^2) dx+ \int_1^2 -(2- x- x^2) dx$