These methods work wrong with negative or non-integral parameters.
==== Here is the minimized test demonstrating the bug ====
import java.lang.Bignum;
class java_lang_Bignum_integerDivide {
  public static void main(String args[]) {
     Bignum b1=new Bignum("35.12");
     Bignum b2=new Bignum("5");
     System.out.println(b1.integerDivide(b2)[0]); // should print 7
     System.out.println(b1.integerDivide(b2)[1]); // should print 0.12
     System.out.println(b1.remainder(b2)); // should print 0.12

     b1=new Bignum("-35");
     b2=new Bignum("5");
     System.out.println(b1.integerDivide(b2)[0]); // should print -7
     System.out.println(b1.integerDivide(b2)[1]); // should print 0
     System.out.println(b1.remainder(b2)); // should print 0

  }
}
===== Here is the output of the test =====
7
.02
.02
0
-35
-35