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Solve 1+11+1 strictly using calculus. DO NOT use simple addition

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Q. Solve 1+11+1 strictly using calculus. DO NOT use simple addition
  1. Interpret as area under curve: We can interpret 1+11+1 as the area under the curve of the function f(x)=1f(x) = 1 from x=0x=0 to x=2x=2 using the definite integral.\newlineCalculate the definite integral of f(x)=1f(x) = 1 from x=0x=0 to x=2x=2.\newline\(\newline\)\int_{\(0\)}^{\(2\)} \(1\) \, dx = [x]_{\(0\)}^{\(2\)}
  2. Calculate definite integral: Evaluate the definite integral at the upper and lower bounds. [x][x] from 00 to 22 = 2−02 - 0
  3. Evaluate at bounds: Simplify the result to find the final answer.\newline2−0=22 - 0 = 2

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