I got an answer but dont know how to show it with the correc

I got an answer but don\'t know how to show it with the correct work. Some correct work would be greatly appreciated.

Solution

f(x)=x^3+6x

inverval is 1 to 4

x=(4-1)/n=3/n

x_i=1+i*3/n

Right riemann sum

Sum (R)= (i=1 to n) f(xi)xi

= (i=1 to n) [[1+i*3/n]^3+6[1+i*3/n]](3/n)

= (i=1 to n) 3/n[1+27i^3/n^3.........]

calculate (its easy)

then find the left riemann sum

x_i-1=1+(i-1)*3/n=3i/n-3/n+1

calculate Sum (L)= (i=1 to n) f(x(i-1))x

put limit n--->infinity

if Sum (R)=Sum (L)=some value :)