Proving Lebesgue Integrability for Uniform Limit Step Functions on [0,1]

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Homework Statement


If f:[a,b] -> C is the uniform limit of step functions (f_n) on [0,1], show that f is Lebesgue integrable


My first question is why on [0,1] and not on [a,b]?
 
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Good question. Must be a typo.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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