Integrate a Discontinuous Piecewise Linear Function

I have the following equation:

y={600   0<=x<15
   1200  15<=x<30
   2400  30<=x<45
   1200  45<=x<60
   600   60<=x<75

I need the cumulative integral as a function of x, both to plot the result and to perform an additional integration. I originally tried defining y as a vector and integrating with trapz:

y(1:15) =600
y(16:30)=1200
...
for j=1:length(y)
int_y=trapz(y(1:j))
end

This obviously gives the incorrect answer, because of the way I defined the intervals, but I'm pretty sure I can't integrate the discontinuities accurately with the trapezoidal rule.

I've switched to integrating each interval individually:

y(1,1:16)=600
y(2,1:16)=1200
...
I haven't worked out the details of a similar loop to integrate each row of the vector and deal with the endpoints yet, but I'm pretty sure I can get the right answer this way.

However, this is messy and awkward.

Am I missing a more straightforward way of performing this integration, either by some better way of defining my intervals or with a more suitable function?

[John D'Errico]

Rectangle rule did not work?

Answer 1

[dpb]

...Am I missing a more straightforward way of performing this integration...

Since the intervals are constants, just define the breakpoints and y values...

>> y=[600 1200 2400 1200 600];
>> dx=16*ones(size(y));
>> cumsum(dx.*y)
ans =
      9600       28800       67200       86400       96000
>>

[Jacob]

I ended up defining y the same way I showed in my question (y(1:15)=600...), but cumsum did the trick!