Answer
$\int\limits_{-1}^1 x^{100} dx=\dfrac{2}{101}$
Work Step by Step
$\int\limits_{-1}^1 x^{100} dx$
This is a single term function. Integrate and use the second part of the fundamental theorem of calculus to get the result:
$\int\limits_{-1}^1 x^{100} dx=\dfrac{1}{101}x^{101}\Big|_{-1}^{1}=\dfrac{1}{101}[(1)^{101}-(-1)^{101}]=...$
$...=\dfrac{1}{101}[1-(-1)]=\dfrac{1}{101}(2)=\dfrac{2}{101}$