`int_(1)^(2)(4x^(3)-5^(2)+6x+9)dx`

Explanation

`int_(1)^(2)(4x^(3)-5x^(2)+6x+9)dx`
`=[(4x^(4))/(4)-(5x^(3))/(3)+(6x^(2))/(2)+9x]_(1)^(2)`
`=[x^(4)-(5x^(3))/(3)+5x^(2)+9x]_(1)^(2)`
`=[(2)^(4)-(5(2)^(3))/(3)+3(2)^(2)+9(2)]-[(1)^(4)-(5(1)^(3))/(3)+3(1)^(2)+9(1)]` ltbr `=(16-(40)/(3)+12+18)-(1-(5)/(3)+3+9)`
`=(98)/(3)-(34)/(3)=(64)/(3)`