The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table.

Time(s) 0 0.5 1 1.5 2 2.5 3
Velocity (ft/sec) 0 6.2 10.8 14.9 18.1 19.4 20.2
a) Find a lower estimate for the distance that she traveled during these 3 seconds.

b) Find an upper estimate for the distance that she traveled during these 3 seconds.