Re: How neuron integrate with different input?

A thorough answer to your question can be found in any general neuroscience 
textbook.  Neuroscience by Kandel and Schwartz is nice.  Here is a general 
answer to your question:

Neurons in our brain communicate with each other via specialized junctions 
called synapses.  Each neuron can receive input from many different 
sources.  These inputs can work to either excite the cell or inhibit the 
cell.  The output of a given neuron is controlled by many things.  Four 
important factors are 1. The types of inputs that it gets (excitatory or 
inhibitory), 2. When does the neuron get the different types of inputs, 3. 
 Where the inputs are on the cell (on the cell body or out on dendrites) 
and how large, physically, the input is, and 4.  What 'state' the neuron is 
in when it receives the inputs.

The balance, timing, and magnitude of excitatory and inhibitory inputs are 
crucial in determining whether a neuron will fire an action potential or 
not.  There are some cells, like the large cells in the cerebral cortex, 
where inhibitory inputs are occurring almost constantly and work to act 
like a counterbalance for the excitation.  This makes sure that only very 
important information gets through (a large excitatory input).  

The magnitude of each input is determined, in part, by how large 
(physically) the input is and where on the postsynaptic cell it ends.  The 
larger the size of the input (the axon terminal) the larger the effect it 
will have in a lot of cases; there will be more neurotransmitter released. 
 In general, if a synapse occurs close to the cell body it will have a 
larger effect than if it occurs on the dendrites.

Each cell has its own personalized resting state (unstimulated) that makes 
it either easy or difficult to change it away from that resting state.  
This is determined by the types of ion channels that it has in its membrane 
and if those ion channels are able to be modulated by substances such as 
neurotransmitters (acetylcholine, norepinephrine, GABA, etc.) and peptides. 
 Some cells, like a few in the auditory system, have many channels that 
pass potassium.  This potassium that is leaking out of the cell (down its 
electrochemical gradient) works to counteract small inputs so that the cell 
will only fire an action potential when there has been a large input.

Important information passes through the nervous system encoded by action 
potentials.  There are two main codes that seem to be used: a rate code 
(frequency) and a temporal code (pattern of action potentials).  A great 
example of single cells that uses both of these codes is neurons in the 
thalamus.  Which code that these cells use seems to be dependent on the 
state of arousal of the animal (humans and nonhuman animals).  These cells 
will fire a series of simple action potentials, using the rate code when 
the animal is paying constant attention to something.  However, when the 
animal perceives something novel, these neurons will fire bursts of action 
potentials. Bursts are 3 or more action potentials that occur at a very 
high frequency and are usually accompanied by a large depolarization caused 
by calcium flowing into the cell.  These two modes will send very different 
signals to the targets of these neurons. The bursts are thought to be an 
initial attention-getter telling parts of the brain "Hey, pay attention!  
There is something new and interesting here."  These bursts, in this 
example, will then be followed by the series of simple action potentials 
(tonic mode).