the distance traveled will be given by where is the curve that passes through all the points given (can you tell me why that is? why does the integral of the graph of the speed give the distance traveled?)

now all we have to do is find the curve that fits. using the method in post #1 here, we realize a quadratic will fit. so we will take

we know that , we can use these to form 3 simultaneous equations to find a,b, and c, and then use the formula i gave you earlier