If you mean the the integral of sin(x2)dx, It can only be represented as an infinite series or a unique set of calculus functions known as the Fresnel Integrals (Pronounced Frenel). These functions, S(x) and C(x) are the integrals of sin(x2) ans cos(x2) respectively. These two integrals have some interesting properties. To find out more, go to:
http://en.wikipedia.org/wiki/Fresnel_integral
I hope this answers your question.
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Do you mean the Convolution Integral?
The integral of -x2 is -1/3 x3 .
2 2x makes no sense. If you meant the integral of 2x, it is x2 + C. If you meant the integral of 4x, it is 2x2 + C. If you meant the integral of 2x2, it is 2/3 x3 + C.
Im still taking Integral Calculus now, but for me, if you dont know Differential Calculus you will not know Integral Calculus, because Integral Calculus need Differential. So, as an answer to that question, ITS FAIR