(a) The particle's speed is the sum of all the areas underneath the curve up to 10 seconds (I'm sure that you've learned that given an acceleration vs. time graph, the area underneath represents the particle's velocity). Note that if the curve is underneath the graph and you're finding speed, you don't take into account that the area is 'negative'.
(b) You have the speed from 0 to 10 seconds, it doesn't move from 10 to 15, and you have its speed from 15 to 20. You should be able to calculate the total distance travelled by considering each 3 cases separately. For example, in the first 10 seconds, if it travels at the speed of x m/s, then the distance travelled is metres (since ).