give an example of a function (other then arctan) which is an
antiderivative of f(x)=1/(1+x^2). use your example to give anexact
evaluation of the area under the curve y=f9x0 for -1 <= x <+ 1

Sorry, but the arctangent is the antiderivative of the function.  Math
doesn't have multiple answers.

Since this question was asked over a month ago, the test was certainly
turned in by now... otherwise I couldn't justify encouraging someone
plagerize my work on a test. But since I'm sure there is no chance of
this any longer, here is a hint in the form of a math joke (I actually
read this joke in a book).

Two math professors are sitting at a bar talking about the general
public. The first professor says, "I bet the average person in here
knows calculus."
The second responded, "I'll bet you $5 our waitress doesn't."
So they agree to ask the following question: what is the
antiderivative of x^2? Of course they agreed the answer was (x^3)/3.
So, they wait for their waitress to come over, and the second
professor says to her, "We're trying to settle a bet. Can you tell us
what the antiderivative of x^2 is?"
The waitress responds, "One-third times x cubed... plus C."