Added integration number

Makefile

@@ -1,2 +1,3 @@
 all:
-	gcc -g -O0 -Wall -Wextra -Wunused -pedantic -std=c99 -lm -o tp3-1 tp3-1.c
+	gcc -g -O2 -Wall -Wextra -Wunused -pedantic -std=c99 -lm -o tp3-1 tp3-1.c
+	gcc -g -O2 -Wall -Wextra -Wunused -pedantic -std=c99 -lm -o tp3-2 tp3-2.c

tp3-2.c

@@ -0,0 +1,47 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+
+
+double IntegrateTrapezoid(double (*f)(double), double start, double end, size_t num_intervals) {
+    double sum = 0.0;
+    double x0 = start;
+    double h = (end - start) / num_intervals;
+
+    for (size_t i = 0; i < num_intervals; ++i) {
+        double y1 = (*f)(x0);
+        double y2 = (*f)(x0 + h);
+
+        sum += (y1 + y2) / 2 * h;
+        x0 += h;
+    }
+
+    return sum;
+}
+
+
+double IntegrateSimpson1_3(double (*f)(double), double start, double end) {
+    double h = (end - start) / 2;
+
+    return h/3 * ((*f)(start) + 4*(*f)(start + h) + (*f)(end));
+}
+
+
+double IntegrateSimpson3_8(double (*f)(double), double start, double end) {
+    double h = (end - start) / 3;
+
+    return 3.0/8.0 * h * ((*f)(start) + 3*(*f)(start + h) +
+                          3*(*f)(start + 2*h) + (*f)(end));
+}
+
+
+double f(double x) {
+    return 1.0 / (x*x + x + 1);
+}
+
+int main(void) {
+    printf("%g\n", IntegrateTrapezoid(&f, 0, 6, 100));
+    printf("%g\n", IntegrateSimpson1_3(&f, 0, 6));
+    printf("%g\n", IntegrateSimpson3_8(&f, 0, 6));
+    return EXIT_SUCCESS;
+}