antiderivative, sigma, and one inflection point?

Question

1.find m and n such that (1,4) is an inflection point of f(x)=mx^3+3nx^2.
2.write the sum using sigma notaion: -(1/2)+(2/3)-(3/4)+(4/5)...-(13/14).
3.summation formula find 40*Sigma*j=1 [(j-2)(j+2)]
4.antiderivative of f(t)=5sint+2cos(t).
5.Integral(cube rootof r^2+(2/r^3)-6) dr
6.integral (x^3-4x)/x^3 dx

I have answered the rest of the questions on these hand outs, but I have no clue of how to do the antiderivatives. I also have about 30 minutes till class. Any help would be appreciated. I cant remember for the life me about sigma. Thanks

Answer 1

4. -cos t + 2sint + C
5. r^3/3 - 1/r^2 -6r + C
6.

Answer 2

1. n=2 m =-2
2. sigma(bottom:n=1 top 13) of [ n/n+1]

6. x = 4/x