Evaluate `int_(0)^(2)(x^2+x+2)dx`

Answer

D

Explanation

`int_(p+m alpha)^(q+n alpha) g(t)dt=int_(p+m alpha)^(p)g(x)dx+int_(p)^(q)g(x)dx+int_(q)^(q+n alpha) g(x)dx`
`=-m/2 int_(0)^(2 alpha) g(x)dx+int_(p)^(q)g(x)dx+n/2 int_(0)^(2alpha) g(x)dx`
`=int_(p)^(q)g(x)dx+((n-m)/2)int_(0)^(2alpha) g(x)dx`