Why do we provide extra reinforcement bars at the end portion of beam?and how we can calculate the amount of reinforcement?

That's for resist diagonal tension stress and in order to prevent inclined cracks to occur by action of maximum shear stresses  which concrete fails to resist

We can calculate the amount of steel reinforcement bars by determining the dead and live loads exerted on the beam or any structures member 

You have more links at the end of your beams to resist shear because shear is usually maximum at the support and decreases as you move away from the support. This can be seen from your shear-force diagram. 

Generally the bending moment diagram would do the reverse of a shear force diagram in that bending would increase as you move away from the support assuming its simply supported you would have a maximum bending at the supports. For continuous beam there is a hogging moment there hence you would need to provide more steel to counteract that moment.

Also how you idealise your element that is if you assume if you beam fully fixed or simply supported or partially fixed then moment redistribution would now affect the amount of reinforcement at the supports.

Steel is good to resist the diagonal negative tension that concrete fail to resist.

We can calculate the amount of the reinforcement through the sheer force diagram.

 

The top reinforcement in the ends of beam above the supports is used to resist the negative bending moment .. 

The additional shear reinforcement "diagonal or vertical" in the ends of beam is used to resist the maximum shear forces affecting on the beam ..

thanks 

By examining the bending moment diagram of a beam it clears that the negative moment occurs at the corners so in that area steel is increased. 

Extra reinforcement bars at end of beam are two types First is top reinforcement at the end of beam to resist negative bending moment at support, it's calculated from bending moment diagram. Second is concentration of links at support to resist shear force, it's calculated from shear force diagram