Simpson's method for e^x sin x + x^2 from 0 to 4 - Wolfram|Alpha
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    Result:

    link to /input/?i=11.7036&lk=1&a=ClashPrefs_*Math-
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    Symbolic form of Simpson's rule:

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    Plot:

    Frame
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    Method comparisons:

    link to /input/?i=left+endpoint+method++2++++x++++++++from+0.+to+4.+with+1+intervals%0A+++++++++++++++++++++x++%2B+E++Sin%5Bx%5D&lk=1link to /input/?i=left+endpoint+method++2++++x++++++++from+0.+to+4.+with+1+intervals%0A+++++++++++++++++++++x++%2B+E++Sin%5Bx%5D&lk=1link to /input/?i=right+endpoint+method++2++++x++++++++from+0.+to+4.+with+1+intervals%0A++++++++++++++++++++++x++%2B+E++Sin%5Bx%5D&lk=1link to /input/?i=right+endpoint+method++2++++x++++++++from+0.+to+4.+with+1+intervals%0A++++++++++++++++++++++x++%2B+E++Sin%5Bx%5D&lk=1link to /input/?i=-101.28&lk=1&a=ClashPrefs_*Math-link to /input/?i=midpoint+method++2++++x++++++++from+0.+to+4.+with+1+intervals%0A++++++++++++++++x++%2B+E++Sin%5Bx%5D&lk=1link to /input/?i=42.8754&lk=1&a=ClashPrefs_*Math-link to /input/?i=trapezoidal+rule++2++++x++++++++from+0.+to+4.+with+1+intervals%0A+++++++++++++++++x++%2B+E++Sin%5Bx%5D&lk=1link to /input/?i=trapezoidal+rule++2++++x++++++++from+0.+to+4.+with+1+intervals%0A+++++++++++++++++x++%2B+E++Sin%5Bx%5D&lk=1link to /input/?i=-50.64&lk=1&a=ClashPrefs_*Math-link to /input/?i=Simpson%27s+rule++2++++x++++++++from+0.+to+4.+with+1+intervals%0A+++++++++++++++x++%2B+E++Sin%5Bx%5D&lk=1link to /input/?i=Simpson%27s+rule++2++++x++++++++from+0.+to+4.+with+1+intervals%0A+++++++++++++++x++%2B+E++Sin%5Bx%5D&lk=1link to /input/?i=11.7036&lk=1&a=ClashPrefs_*Math-link to /input/?i=Boole%27s+rule++2++++x++++++++from+0.+to+4.+with+1+intervals%0A+++++++++++++x++%2B+E++Sin%5Bx%5D&lk=1link to /input/?i=Boole%27s+rule++2++++x++++++++from+0.+to+4.+with+1+intervals%0A+++++++++++++x++%2B+E++Sin%5Bx%5D&lk=1link to /input/?i=19.346&lk=1&a=ClashPrefs_*Math-
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    Mathematica input:

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    Download full output as:

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