Junit Test method giving an error due to an Unhandled Exception Type

I am writing a Java Unit test for one of my method. The method declaration is like this:

public int convertToInteger() throws InvalidRomanNumberException
{
    int result=0;
    BaseRomanNumeral num1, num2; 
    int i=0;
    if(!validOperation())
        throw new InvalidRomanNumberException();
}

Now I am trying to write two unit tests. One is to test if the right exception is thrown. Another one is to make sure that that the write conversion happens. This is how my test case looks

@Test
public void testRomanNumberConversion() {
    String romanValue="MCMII";
    RomanNumber num=new RomanNumber(romanValue);
    assertEquals(1903,num.convertToInteger());  
}

@Test(expected = InvalidRomanNumberException.class)
public void testInvalidRomanNumberExceptionThrown()  {
    String romanValue="MCMIIII";
    RomanNumber num=new RomanNumber(romanValue);
    num.convertToInteger(); 
}

For both these test cases I am getting an error saying Unhandled InvalidRomanNumberException. This is resolved only when I add throws InvalidRomanNumberException to each method definition. But I don't think that is the right way. Just want to check with the rest of you, what is the norm here? How should I resolve this unhandled exception message