Husk, (削除) 10 (削除ここまで) 9 bytes

-1 byte thanks to Zgarb

uSȯf¬`Bṁṡ

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###Explanation

 ṁṡ Concatenate together the symmetric ranges of each coefficient
 (It is guaranteed that the integer roots lie in the range [-n..n],
 where n is the coefficient with the largest magnitude)
 Sȯf Find all the values in that range which
 ¬ are zero
 `B when plugged through the polynomial
 (Base conversion acts as polynomial evaluation)
u De-duplicate the roots

Husk, (削除) 10 (削除ここまで) 9 bytes

-1 byte thanks to Zgarb

uSȯf¬`Bṁṡ

Try it online!

Explanation

 ṁṡ Concatenate together the symmetric ranges of each coefficient
 (It is guaranteed that the integer roots lie in the range [-n..n],
 where n is the coefficient with the largest magnitude)
 Sȯf Find all the values in that range which
 ¬ are zero
 `B when plugged through the polynomial
 (Base conversion acts as polynomial evaluation)
u De-duplicate the roots

Husk, 10 bytes

Sȯf¬`Boṡ►a

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###Explanation

 ►a Get the coefficient with the largest absolute value: n
 oṡ Get the range [-n..n]
Sȯf Find all the values in that range which
 ¬ are zero
 `B when plugged through the polynomial
 (Base conversion acts as polynomial evaluation)

Husk, (削除) 10 (削除ここまで) 9 bytes

-1 byte thanks to Zgarb

uSȯf¬`Bṁṡ

Try it online!

###Explanation

 ṁṡ Concatenate together the symmetric ranges of each coefficient (It is guaranteed that the integer roots lie in the range [-n..n],
 where n is the coefficient with the largest magnitude)
 Sȯf Find all the values in that range which
 ¬ are zero
 `B when plugged through the polynomial
 (Base conversion acts as polynomial evaluation)
u De-duplicate the roots