(1)

When you integrate a constant zero over any interval, you’re essentially calculating the area under a flat line sitting on the x-axis. So, when you compute , the result is simply , where is the constant of integration. Imagine a blank canvas—no paint (or area)—no matter how wide or tall it is!

But where’s the excitement, right? The fun part comes in understanding that anytime you’re integrating zero, the output is always just a reflection of your chosen interval. So, if you ever find yourself integrating zero across a span of time, space, or imagination, you get the blissful certainty that the answer is beautifully simple!