Question

Can someone please help explain in detail how the solution is obtained for 3B-5 in problem set 6 (on the integration worksheet)?

Here's the problem:

Evaluate the limit by relating it to a Riemann sum.

the limit as n tends to infinity of (sin(b/n)+sin(2b/n)+...+sin((n-1)b/n)+sin(nb/n))/n

The solution is the definite integral from 0 to 1 of sin(bx)dx