Can any rational number be an integer?

No, only a rational number is not a fraction or decimal. But any whole number including one with a negative sign.

For example, - 1 and 1 could be a integer.

Yes every integer is a rational number, since each integer can be written in the form n/1. For example 5 = 5/1 and thus 5 is a rational number. However, numbers like 1/2, 45454737/2424242, and - 3/7 are also rational, since they are fractions whose numerator and denominator are integers.