Answer
3/2
Work Step by Step
$\int$(1-x) from -1 to 2:
Find the integral of each part of f(x) using the formula $\int x^{n} = 1/(n+1) x^{n+1}$:
$\int 1$=1x
$\int x=x^{2}/2$
Therefore $\int (1-x) = (x-x^{2}/2)$
To find the area from -1 to 2, find f(2)-f(-1), with f(x) being the newly found integral
$(2-2^{2}/2)-(-1-1^{2}/2)$
=3/2