Rewards and returns

As we have learned, in an RL environment, an agent interacts with the environment by performing an action and moves from one state to another. Based on the action it performs, it receives a reward. A reward is nothing but a numerical value, say, +1 for a good action and -1 for a bad action. How do we decide if an action is good or bad? In a maze game, a good action is where the agent makes a move so that it doesn't hit a maze wall, whereas a bad action is where the agent moves and hits the maze wall. 

An agent tries to maximize the total amount of rewards (cumulative rewards) it receives from the environment instead of immediate rewards. The total amount of rewards the agent receives from the environment is called returns. So, we can formulate total amount of rewards (returns) received by the agents as follows:

 is the reward received by the agent at a time step  while performing an action
to move from one state to another.  is the reward received by the agent at a time
step  while performing an action to move from one state to another. Similarly,  is the reward received by the agent at a final time step  while performing an action to move from one state to another.