Question

Question attached as screenshot, please help me I am paying close attention

Answer 1

`\int ((x^3)/(4)+(2x^2)/(3)-1)dx`

Take the integral of each

`\int (x^3)/(4)dx+\int (2x^2)/(3)dx-\int 1dx`
`\int (x^3)/(4)dx=(x^4)/(16)`
`\int (2x^2)/(3)dx=(2x^3)/(9)`
`\int 1dx=x`

Now properly combine them back

`(x^4)/(16)+(2x^3)/(9)-x+c`

The final answer

Option D