Design a C$++$ program that prompts the user to input the final exam grades of six students. After receiving the data, the program should analyze it and display the student with the highest grade as well as the student with the lowest grade. Implement a class named 'Student' with two data members: a string to store the student's name and an integer to store their grade. The class should include a parameterized constructor to assign values to the data members of a 'Student' object, and remember to create a destructor.

Within the main function, create an array of six elements of type 'Student', ensuring that values are assigned to the data members of each element in the array.

Additionally, create two functions to perform the analysis. One function should return the index of the student with the highest grade, while the other function should return the index of the student with the lowest grade.

Please note that along with the project code, you need to test your project and provide the results of its execution. You can submit the answer using either a CPP file or a text file.