Suppose I was integrating some function across the interval [a,d].

Suppose, though, that this function was a piecewise function defined as follows:

Where u and v are some constants.

So the integral looks something like this:

Is there some way to express this as a single integral across the whole interval [a,c]?

I tried equating my general integral to and solved for w, but the answer would require that I'd have to compute the individiual integrals first before I could combine them. Which makes it rather pointless.

The reason I ask is that I'm integrating some pretty big, nasty functions, and it would save me a lot of time under exam conditions if I didn't have to write each integral out twice - it seems to me to be a perfect waste of time when they're both the same function being integrated over adjacent intervals!