Evaluate the integral(x^e + e^x) from (-1 to 1)

I'm getting hung up when I take the antiderivative of x^e, I get x^(e+1)/(e+1). But when I plug -1 into this my calculator gets an error. Upon further review, it seems -1 is out of the domain of f(x) = x^e + e^x. So....when integrating, do I only go from 0 to 1 since anything less than 0 does not exist?

NOTE: I'm interested in explanations only, not just answers, and not links to wolfamalpha.com.

I think you'd have to say this integral doesn't exist. Think about how the integral is defined in terms of a Riemann sum which requires f(x1), f(x2), ... f(xn) at intervals from -1 to 1. Some of those values don't exist, so the Riemann sum doesn't exist, so the limit of the sum which is the integral doesn't exist.

I'm not going to link to it, because you told me not to. But Wolfram gives me an answer of

e - 1/e + ( 1 + cos(eπ) + sin(eπ)√-1 )/(1+e)

or about

2.44904+0.208145√-1

The cheeky answer is that your calculator isn't expensive enough to do this integral. The serious answer is that you've stumbled upon a very deep question in mathematics that is omitted from the standard curriculum, because of prejudice against a beautiful number that was slandered four centuries ago by the word 'imaginary'.

Of course, the *practical* answer is that if -1 isn't in the domain of x^e, then you shouldn't try to do any surgery without your teachers permission. Just write "the integral from -1 to 1 is not defined, and here's why. However, the integral from 0 to 1 is well-defined and its value is ____."