3
x^3/3 - x^2 + 3x ] =
-2
[ 3^3/3 - (3)^2 + 3(3) ] - ( -2)^3/3 - (-2)^2 + 3(-2) ] =
[ 9 - 9 + 9 ] - [ -8/3 - 4 - 6 ] =
9 + 8/3 + 4 + 6 =
65/3
\(\int _{-2}^3x^2-2x+3dx\)
\(=\int _{-2}^3x^2dx-\int _{-2}^32xdx+\int _{-2}^33dx\)
\(=\frac{35}{3}-5+15\)
\(=\frac{65}{3}\)
.