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(1) Set up the Riemann sums for the following functions over the given intervals. Then, after setting them up, compute the Riemann sum. (Feel free to use a computer or calculator to compute the Riemann sum after you set it up. You need to show your setup to get full points.) (a) \( R_{6} \) for \( f(x)=x^{3}+1 \) from \( x=2 \) to \( x=5 \). (b) \( L_{4} \) for \( f(x)=x^{2}+x \) from \( x=-2 \) to \( x=2 \). (c) \( L_{8} \) for \( f(x)=\sin x \) from \( x=0 \) to \( x=2 \pi \) (2) Alice and Bob write some code to compute the right Riemann sum \( R_{n} \) of the integral \( \int_{0}^{1} x^{2} d x \) for any \( n \). When Alice uses her code to compute \( R_{1000000000} \), she gets \( 0.333333333 \). When Bob runs his code to compute \( R_{1000000000} \), he gets \( 4.000000001 \). Whose code is more likely to be correct? Why?