Let y=f(x). The lower sum is that area above the x-axis. When x2-25=0, x=5 is the x-intercept on the right of the y-axis. This is the upper limit for the integration and 0 is the low limit:
Area =∫[0,5]ydx=∫[0,5](25-x2)dx=[25x-x3/3]05.
So area =(125-125/3)=250/3 square units (83.33).