I have three solutions for this problem :
First
In your code you are using keyboard.next() which will return a string that you have to convert it into Integer. For that you can use keyboard.nextInt(), it will directly convert the string into integer.
import java.util.Scanner;
public class strings {
    public static void main(String[] args) {
        Scanner keyboard = new Scanner(System.in);
        System.out.print("Type your first integer: ");
        int first = keyboard.nextInt();
        System.out.print("Type your seconds integer : ");
        int second = keyboard.nextInt();
        System.out.print("The sum of your two integers are:"+(first+second));
    }
}
Second
or you can convert the string into Integer by using  Integer.parseInt(**String to be converted to Integer**), this will convert the string into Integer.
import java.util.Scanner;
public class strings {
    public static void main(String[] args) {
        Scanner keyboard = new Scanner(System.in);
        System.out.print("Type your first integer: ");
        int first = Integer.parseInt(keyboard.next());
        System.out.print("Type your seconds integer : ");
        int second = Integer.parseInt(keyboard.next());
        System.out.print("The sum of your two integers are:"+(first+second));
    }
}
Third
or you can convert the string into Integer by using  Integer.valueOf(**String to be converted to Integer**), this will convert the string into Integer.
import java.util.Scanner;
public class strings {
    public static void main(String[] args) {
        Scanner keyboard = new Scanner(System.in);
        System.out.print("Type your first integer: ");
        int first = Integer.valueOf(keyboard.next());
        System.out.print("Type your seconds integer : ");
        int second = Integer.valueOf(keyboard.next());
        System.out.print("The sum of your two integers are:"+(first+second));
    }
}