Object is, haha, an object type, while int is a primitive type. You cannot translate objects to ints through direct casts; but if the object is of Integer, you could access and call the member method intValue() which returns the actual integer value being wrapped.
Example:
public void A(Object o) {
if(o instanceof Integer)
B(((Integer) o).intValue());
else
throw new IllegalArgumentException();
}
public void B(int i) {
/*
code is here
*/
}