You need to enclose that in <%! %> as follows:
<%!
public String getQuarter(int i){
String quarter;
switch(i){
        case 1: quarter = "Winter";
        break;
        case 2: quarter = "Spring";
        break;
        case 3: quarter = "Summer I";
        break;
        case 4: quarter = "Summer II";
        break;
        case 5: quarter = "Fall";
        break;
        default: quarter = "ERROR";
}
return quarter;
}
%>You can then invoke the function within scriptlets or expressions:
<%
     out.print(getQuarter(4));
%>or
<%= getQuarter(17) %>