Integrability of monotonic decreasing function

Hello, I have to prove for a monotonic decreasing function f(x) on , [0,4] prove that the integral from 0 to 4 f(x)dx exists. The proof I have is similar to this:

*Proof.* *If f is constant, then we are done. We prove the case for f monotone increasing. The case for monotone decreasing is similiar. We again use the condition (*) to prove that f is Riemann-integrable. If http://www.math.sc.edu/%7Esharpley/m...54_9/img37.gif , we set http://www.math.sc.edu/%7Esharpley/m...54_9/img65.gif and consider any partition P with http://www.math.sc.edu/%7Esharpley/m...54_9/img62.gif . Since f is monotone increasing on [a,b], then http://www.math.sc.edu/%7Esharpley/m...54_9/img66.gif and http://www.math.sc.edu/%7Esharpley/m...54_9/img67.gif . Hence *

http://www.math.sc.edu/%7Esharpley/m...54_9/img68.gif

How does this change for a decreasing function? Does the partition in anyway change?