This question requires us to:

1) Find the integral and then write the upper and lower limits with square brackets, as follows:

`[x^3+2x^2+x]_1^5`

The upper and lower limits are written like this to mean they will be substituted into the expression in brackets.

2) Next, substitute `5` (the upper limit) into the integral:

`[(5)^3+ 2(5)^2+ 5] = ` `125 + 50 + 5 = 180`

3) Then substitute `1` into the integral:

`[(1)^3+ 2(1)^2+ 1] = ` `1 + 2 + 1 = 4`

4) Subtract the result of (3) from the result of (2) for our final answer:

`180 − 4 = 176`

Normally, we would write our complete solution as follows:

`int_1^5(3x^2+4x+1)dx=[x^3+2x^2+x]_1^5`

`=[(5)^3+ 2(5)^2+ 5]-` `[(1)^3+ 2(1)^2+ 1]`

`=180 − 4 `

`= 176`