So this behavior isn't documented, so it's hard to say wether it's correct:
Integer(arg, base=0, exception: true) → integer or nil
Converts arg to an Integer. Numeric types are converted directly (with floating point numbers being truncated). base (0, or between 2 and 36) is a base for integer string representation. If arg is a String, when base is omitted or equals zero, radix indicators (0, 0b, and 0x) are honored. In any case, strings should consist only of one or more digits, except for that a sign, one underscore between two digits, and leading/trailing spaces are optional. This behavior is different from that of String#to_i. Non string values will be converted by first trying to_int, then to_i.
Passing nil raises a TypeError, while passing a String that does not conform with numeric representation raises an ArgumentError. This behavior can be altered by passing exception: false, in this case a not convertible value will return nil.
However the intent of the implementation is fairly clear:
static VALUE rb_convert_to_integer(VALUE val, int base, int raise_exception) { VALUE tmp; // snip if (RB_FLOAT_TYPE_P(val)) { double f = RFLOAT_VALUE(val); if (!raise_exception && !isfinite(f)) return Qnil; if (FIXABLE(f)) return LONG2FIX((long)f); return rb_dbl2big(f); } else if (RB_INTEGER_TYPE_P(val)) { return val; } else if (RB_TYPE_P(val, T_STRING)) { return rb_str_convert_to_inum(val, base, TRUE, raise_exception); } else if (NIL_P(val)) { if (!raise_exception) return Qnil; rb_raise(rb_eTypeError, "can't convert nil into Integer"); } tmp = rb_protect(rb_check_to_int, val, NULL); if (RB_INTEGER_TYPE_P(tmp)) return tmp; rb_set_errinfo(Qnil); if (!raise_exception) { VALUE result = rb_protect(rb_check_to_i, val, NULL); rb_set_errinfo(Qnil); return result; } return rb_to_integer(val, "to_i", idTo_i); }
If passed an object that is neither a direct string nor a native numeric, Integer first tries to invoke to_int, then fallback to invoke to_i.
I suppose a case could be made to first try to call to_str.