`int_1^4(5-2t+3t^2)dt`

apply the sum rule and power rule,

`=[5t-2t^2/2+3t^3/3]_1^4`

`=[5t-t^2+t^3]_1^4`

`=[5*4-4^2+4^3]-[5*1-1^2+1^3]`

`=(20-16+64)-(5-1+1)`

`=(84-16)-(5)`

=63

`int_1^4(5-2t+3t^2)dt`

apply the sum rule and power rule,

`=[5t-2t^2/2+3t^3/3]_1^4`

`=[5t-t^2+t^3]_1^4`

`=[5*4-4^2+4^3]-[5*1-1^2+1^3]`

`=(20-16+64)-(5-1+1)`

`=(84-16)-(5)`

=63