想问下关于曲线面积的求法

ListPlot[{{-60, 56.0055}, {-50, 54.8688}, {-40, 50.2206}, {-37.5,
48.6125}, {-35, 46.7932}, {-32.5, 44.7469}, {-30, 42.4642}, {-27.5,
39.9453}, {-25, 37.1687}, {-22.5, 34.1187}, {-20,
30.8087}, {-17.5, 27.2796}, {-15, 23.6091}, {-12.5, 19.9112}, {-10,
16.3325}, {-7.5, 13.0149}, {-5, 10.0223}, {-2.5, 7.24017}, {0,
4.29307}, {2.5, 0.470158}, {5, 5.31596}, {7.5, 14.6363}, {10,
29.9744}, {12.5, 55.5239}, {15, 99.4038}, {17.5, 158.412}, {20,
393.752}, {22.5, 802.833}, {25, 1201.03}, {27.5, 1746.65}, {30,
2331.86}, {32.5, 2707.75}, {35, 2828.3}, {37.5, 2840.21}, {40,
2647.03}, {50, 1797.12}, {60, 1071.47}, {70, 702.575}},
Joined -> True, InterpolationOrder -> 3, PlotStyle -> {Red}]
如下所示是用散点画出的曲线，想求它和x=20,x=60以及x轴围成图形的面积，找了很久不知道怎么弄，希望有人能够解答

要不先拟合一下？毕竟散点图画出来了但是没有函数没办法积分吧。。。

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我觉得可以先插值……
f = Interpolation[{{-60, 56.0055}, {-50, 54.8688}, {-40,
50.2206}, {-37.5, 48.6125}, {-35, 46.7932}, {-32.5,
44.7469}, {-30, 42.4642}, {-27.5, 39.9453}, {-25,
37.1687}, {-22.5, 34.1187}, {-20, 30.8087}, {-17.5,
27.2796}, {-15, 23.6091}, {-12.5, 19.9112}, {-10, 16.3325}, {-7.5,
13.0149}, {-5, 10.0223}, {-2.5, 7.24017}, {0, 4.29307}, {2.5,
0.470158}, {5, 5.31596}, {7.5, 14.6363}, {10, 29.9744}, {12.5,
55.5239}, {15, 99.4038}, {17.5, 158.412}, {20, 393.752}, {22.5,
802.833}, {25, 1201.03}, {27.5, 1746.65}, {30, 2331.86}, {32.5,
2707.75}, {35, 2828.3}, {37.5, 2840.21}, {40, 2647.03}, {50,
1797.12}, {60, 1071.47}, {70, 702.575}}, InterpolationOrder -> 2]
NIntegrate[f[x], {x, 20, 60}]
结果是76485.1

data = {{-60, 56.0055}, {-50, 54.8688}, {-40, 50.2206}, {-37.5,
48.6125}, {-35, 46.7932}, {-32.5, 44.7469}, {-30, 42.4642}, {-27.5,
39.9453}, {-25, 37.1687}, {-22.5, 34.1187}, {-20,
30.8087}, {-17.5, 27.2796}, {-15, 23.6091}, {-12.5, 19.9112}, {-10,
16.3325}, {-7.5, 13.0149}, {-5, 10.0223}, {-2.5, 7.24017}, {0,
4.29307}, {2.5, 0.470158}, {5, 5.31596}, {7.5, 14.6363}, {10,
29.9744}, {12.5, 55.5239}, {15, 99.4038}, {17.5, 158.412}, {20,
393.752}, {22.5, 802.833}, {25, 1201.03}, {27.5, 1746.65}, {30,
2331.86}, {32.5, 2707.75}, {35, 2828.3}, {37.5, 2840.21}, {40,
2647.03}, {50, 1797.12}, {60, 1071.47}, {70, 702.575}}
f = Interpolation[data, Method -> "Hermite"]
S = Integrate[f[x], {x, 20, 60}]

直接当多边形算
Area@Polygon@{{20, 393.752}, {22.5, 802.833}, {25, 1201.03}, {27.5,
1746.65}, {30, 2331.86}, {32.5, 2707.75}, {35, 2828.3}, {37.5,
2840.21}, {40, 2647.03}, {50, 1797.12}, {60, 1071.47}, {60,
0}, {20, 0}}

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