diff --git a/education/math/MATH1210 (calc 1)/Integrals.md b/education/math/MATH1210 (calc 1)/Integrals.md
index ffb807f..b9c90cd 100644
--- a/education/math/MATH1210 (calc 1)/Integrals.md	
+++ b/education/math/MATH1210 (calc 1)/Integrals.md	
@@ -143,10 +143,18 @@ $$ \text{length of a curve} = \lim_{n \to \infty} \sum_{i=1}^{n}(\sqrt{(x_i - x_
 	This can also be described as:
 $$ \text{length of a curve} = \lim_{n \to \infty} \sum_{i=1}^{n}(\sqrt{(\Delta x)^2 +(\Delta y)^2}) $$
 2. Using the mean value theorem:
-$$ \lim_{n \to \infty} \sum_{i = 1}^n)\sqrt{\Delta x^2 + (F(x_i) - F(x_{i-1}))i^2} $$
+$$ \lim_{n \to \infty} \sum_{i = 1}^n)\sqrt{\Delta x^2 + (f(x_i) - f(x_{i-1}))i^2} $$
 $$ \lim_{n \to \infty} \sum_{i=1}^n \sqrt{\Delta x ^2 + (f'(x_{\hat{i}}))(x_i - x_{i-1})^2}$$
 3. Factoring out $\Delta x$
-$$ \lim_{n \to \infty} \sum_{i=1}^n \sqrt{x^2(1 + f'(\Delta x_{\hat{i}}))}$$
+$$ \lim_{n \to \infty} \sum_{i=1}^n \sqrt{\Delta x^2(1 + f'(x_{\hat{i}}))}$$
 4. Moving $\Delta x$ out of the root
 
-$$ \lim_{n \to \infty} \sum_{i=1}^n \sqrt{x^2(1 + f'(\Delta x_{\hat{i}}))}$$
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+$$ \lim_{n \to \infty} \sum_{i=1}^n \sqrt{(1 + f'(x_{\hat{i}}))} \Delta x$$
+5. As an integral:
+$$ L =\int_a^b \sqrt{1 + f'(x)^2} dx$$
+## Examples
+> Find the length of the curve $y = -\frac{5}{12}x + \frac{7}{12}$ from the point $(-1, 1)$
+
+1. $L = \int_{-1}^8 \sqrt{1 + (-\frac{5}{12})^2} dx$ 
+2. $= \int_{-1}^8 \sqrt{1 + \frac{25}{144}} dx$ 
+3. = $\int_{-1}^8 \sqrt{\frac{169}{144}}
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