Write a Python program to calculate the total duration of a sequence of up to five TV episodes. The length for each episode is 21 minutes for episode one, 22 minutes for episode two, 23 minutes for episode three, 24 minutes for episode four and 25 minutes for episode five. 

The program should ask the user what is the first and last episode the user would like to watch. The program should then calculate how long it would take to watch the first and last episode, and all the episodes in between. Assume the user enters valid input. You are NOT required to do validation checks of the data input.

Your program should display the total duration of all the episodes in the sequence they have chosen.

Sample program run (user input is given in bold):

Which episode would you like to watch first?    2

Which episode would you like to watch last?    5

The total duration of all episodes is 94 minutes.